Giới hạn Laplace – Wikipedia tiếng Việt

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[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Đăng nhập</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Trang dành cho người dùng chưa đăng nhập <a href="/wiki/Tr%E1%BB%A3_gi%C3%BAp:Gi%E1%BB%9Bi_thi%E1%BB%87u" aria-label="Tìm hiểu thêm về sửa đổi"><span>tìm hiểu thêm</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:%C4%90%C3%B3ng_g%C3%B3p_c%E1%BB%A7a_t%C3%B4i" title="Danh sách các sửa đổi được thực hiện qua địa chỉ IP này [y]" accesskey="y"><span>Đóng góp</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Th%E1%BA%A3o_lu%E1%BA%ADn_t%C3%B4i" title="Thảo luận với địa chỉ IP này [n]" accesskey="n"><span>Thảo luận cho địa chỉ IP 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class="vector-pinnable-header-label">Nội dung</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">chuyển sang thanh bên</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ẩn</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Đầu</div> </a> </li> <li id="toc-Tính_chất" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tính_chất"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Tính chất</span> </div> </a> <ul id="toc-Tính_chất-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Xem_thêm" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Xem_thêm"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Xem thêm</span> </div> </a> <ul id="toc-Xem_thêm-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tham_khảo" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tham_khảo"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Tham khảo</span> </div> </a> <ul id="toc-Tham_khảo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Liên_kết_ngoài" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Liên_kết_ngoài"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Liên kết ngoài</span> </div> </a> <ul id="toc-Liên_kết_ngoài-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Nội dung" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Đóng mở mục lục" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Đóng mở mục lục</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Giới hạn Laplace</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Xem bài viết trong ngôn ngữ khác. Bài có sẵn trong 7 ngôn ngữ" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-7" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">7 ngôn ngữ</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Laplace_limit" title="Laplace limit – Tiếng Anh" lang="en" hreflang="en" data-title="Laplace limit" data-language-autonym="English" data-language-local-name="Tiếng Anh" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Constante_limite_de_Laplace" title="Constante limite de Laplace – Tiếng Pháp" lang="fr" hreflang="fr" data-title="Constante limite de Laplace" data-language-autonym="Français" data-language-local-name="Tiếng Pháp" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%9D%BC%ED%94%8C%EB%9D%BC%EC%8A%A4_%EA%B7%B9%ED%95%9C" title="라플라스 극한 – Tiếng Hàn" lang="ko" hreflang="ko" data-title="라플라스 극한" data-language-autonym="한국어" data-language-local-name="Tiếng Hàn" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Limite_di_Laplace" title="Limite di Laplace – Tiếng Italy" lang="it" hreflang="it" data-title="Limite di Laplace" data-language-autonym="Italiano" data-language-local-name="Tiếng Italy" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D1%80%D0%B5%D0%B4%D0%B5%D0%BB_%D0%9B%D0%B0%D0%BF%D0%BB%D0%B0%D1%81%D0%B0" title="Предел Лапласа – Tiếng Nga" lang="ru" hreflang="ru" data-title="Предел Лапласа" data-language-autonym="Русский" data-language-local-name="Tiếng Nga" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%93%D1%80%D0%B0%D0%BD%D0%B8%D1%86%D1%8F_%D0%9B%D0%B0%D0%BF%D0%BB%D0%B0%D1%81%D0%B0" title="Границя Лапласа – Tiếng Ukraina" lang="uk" hreflang="uk" data-title="Границя Лапласа" data-language-autonym="Українська" data-language-local-name="Tiếng Ukraina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%8B%89%E6%99%AE%E6%8B%89%E6%96%AF%E6%A5%B5%E9%99%90" title="拉普拉斯極限 – Tiếng Trung" lang="zh" hreflang="zh" data-title="拉普拉斯極限" data-language-autonym="中文" data-language-local-name="Tiếng Trung" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q2994928#sitelinks-wikipedia" title="Sửa liên kết giữa ngôn ngữ" class="wbc-editpage">Sửa liên kết</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Không gian tên"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace" title="Xem bài viết [c]" accesskey="c"><span>Bài viết</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Th%E1%BA%A3o_lu%E1%BA%ADn:Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&action=edit&redlink=1" rel="discussion" class="new" title="Thảo luận về trang này (trang không tồn tại) [t]" accesskey="t"><span>Thảo luận</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Thay đổi biến thể ngôn ngữ" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tiếng Việt</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Giao diện"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace"><span>Đọc</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&veaction=edit" title="Sửa đổi trang này [v]" accesskey="v"><span>Sửa đổi</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&action=edit" title="Sửa đổi mã nguồn của trang này [e]" accesskey="e"><span>Sửa mã nguồn</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&action=history" title="Các phiên bản cũ của trang này [h]" accesskey="h"><span>Xem lịch sử</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Công cụ trang"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Công cụ" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Công cụ</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Công cụ</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">chuyển sang thanh bên</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">ẩn</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Thêm tùy chọn" > <div class="vector-menu-heading"> Tác vụ </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace"><span>Đọc</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&veaction=edit" title="Sửa đổi trang này [v]" accesskey="v"><span>Sửa đổi</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&action=edit" title="Sửa đổi mã nguồn của trang này [e]" accesskey="e"><span>Sửa mã nguồn</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&action=history"><span>Xem lịch sử</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Chung </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Li%C3%AAn_k%E1%BA%BFt_%C4%91%E1%BA%BFn_%C4%91%C3%A2y/Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace" title="Các trang liên kết đến đây [j]" accesskey="j"><span>Các liên kết đến đây</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Thay_%C4%91%E1%BB%95i_li%C3%AAn_quan/Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace" rel="nofollow" title="Thay đổi gần đây của các trang liên kết đến đây [k]" accesskey="k"><span>Thay đổi liên quan</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Trang_%C4%91%E1%BA%B7c_bi%E1%BB%87t" title="Một danh sách chứa tất cả trang đặc biệt [q]" accesskey="q"><span>Trang đặc biệt</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&oldid=69563934" title="Liên kết thường trực đến phiên bản này của trang"><span>Liên kết thường trực</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&action=info" title="Thêm chi tiết về trang này"><span>Thông tin trang</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%B7c_bi%E1%BB%87t:Tr%C3%ADch_d%E1%BA%ABn&page=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&id=69563934&wpFormIdentifier=titleform" title="Hướng dẫn cách trích dẫn trang này"><span>Trích dẫn trang này</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%B7c_bi%E1%BB%87t:UrlShortener&url=https%3A%2F%2Fvi.wikipedia.org%2Fwiki%2FGi%25E1%25BB%259Bi_h%25E1%25BA%25A1n_Laplace"><span>Lấy URL ngắn gọn</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%B7c_bi%E1%BB%87t:QrCode&url=https%3A%2F%2Fvi.wikipedia.org%2Fwiki%2FGi%25E1%25BB%259Bi_h%25E1%25BA%25A1n_Laplace"><span>Tải mã QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> In và xuất </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%B7c_bi%E1%BB%87t:S%C3%A1ch&bookcmd=book_creator&referer=Gi%E1%BB%9Bi+h%E1%BA%A1n+Laplace"><span>Tạo một quyển sách</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%B7c_bi%E1%BB%87t:DownloadAsPdf&page=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&action=show-download-screen"><span>Tải dưới dạng PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&printable=yes" title="Bản để in ra của trang [p]" accesskey="p"><span>Bản để in ra</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Tại dự án khác </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q2994928" title="Liên kết đến khoản mục kết nối trong kho dữ liệu [g]" accesskey="g"><span>Khoản mục Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Công cụ trang"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Giao diện"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Giao diện</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">chuyển sang thanh bên</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ẩn</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Bách khoa toàn thư mở Wikipedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="vi" dir="ltr"><p>Trong <a href="/wiki/To%C3%A1n_h%E1%BB%8Dc" title="Toán học">toán học</a>, <b>giới hạn Laplace</b>, <b>hằng số Laplace</b> hay <b>hằng số giới hạn Laplace</b> là giá trị <a href="/wiki/T%C3%A2m_sai" class="mw-redirect" title="Tâm sai">tâm sai</a> lớn nhất mà nghiệm của <a href="/w/index.php?title=Ph%C6%B0%C6%A1ng_tr%C3%ACnh_Kepler&action=edit&redlink=1" class="new" title="Phương trình Kepler (trang không tồn tại)">phương trình Kepler</a> tồn tại, và được biểu diễn dưới dạng một chuỗi <a href="/wiki/L%C5%A9y_th%E1%BB%ABa" title="Lũy thừa">lũy thừa</a> của tâm sai. Giá trị của nó là </p> <dl><dd><span style="white-space:nowrap">0.66274<span style="margin-left:0.25em">34193</span><span style="margin-left:0.25em">49181</span><span style="margin-left:0.25em">58097</span><span style="margin-left:0.25em">47420</span><span style="margin-left:0.25em">97109</span><span style="margin-left:0.25em">25290…</span></span> (dãy số <span class="nowrap"><a href="//oeis.org/A033259" class="extiw" title="oeis:A033259">A033259</a></span> trong bảng <a href="/wiki/B%E1%BA%A3ng_tra_c%E1%BB%A9u_d%C3%A3y_s%E1%BB%91_nguy%C3%AAn_tr%E1%BB%B1c_tuy%E1%BA%BFn" title="Bảng tra cứu dãy số nguyên trực tuyến">OEIS</a>).</dd></dl> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Tính_chất"><span id="T.C3.ADnh_ch.E1.BA.A5t"></span>Tính chất</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&veaction=edit&section=1" title="Sửa đổi phần “Tính chất”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&action=edit&section=1" title="Sửa mã nguồn tại đề mục: Tính chất"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/w/index.php?title=Ph%C6%B0%C6%A1ng_tr%C3%ACnh_Kepler&action=edit&redlink=1" class="new" title="Phương trình Kepler (trang không tồn tại)">Phương trình Kepler</a> biểu diễn mối quan hệ giữa các tính chất hình học của quỹ đạo một vật thể chịu tác dụng của một lực xuyên tâm. Nó có dạng: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M=E-e\sin E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>=</mo> <mi>E</mi> <mo>−</mo> <mi>e</mi> <mi>sin</mi> <mo>⁡</mo> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M=E-e\sin E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92f49670f292ad45dd2311f04742ed4c790a385a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:16.646ex; height:2.343ex;" alt="{\displaystyle M=E-e\sin E}"></span>,</dd></dl> <p>trong đó <span class="texhtml mvar" style="font-style:italic;">M</span> là <a href="/wiki/%C4%90%E1%BB%99_b%E1%BA%A5t_th%C6%B0%E1%BB%9Dng_trung_b%C3%ACnh" class="mw-redirect" title="Độ bất thường trung bình">độ bất thường trung bình</a>, <span class="texhtml mvar" style="font-style:italic;">E</span> là <a href="/wiki/%C4%90%E1%BB%99_b%E1%BA%A5t_th%C6%B0%E1%BB%9Dng_l%E1%BB%87ch_t%C3%A2m" class="mw-redirect" title="Độ bất thường lệch tâm">độ bất thường lệch tâm</a> của một vật thể di chuyển theo quỹ đạo hình <a href="/wiki/El%C3%ADp" class="mw-redirect" title="Elíp">elíp</a> với tâm sai <span class="texhtml mvar" style="font-style:italic;">e</span>. Phương trình này không thể giải tìm <span class="texhtml mvar" style="font-style:italic;">E</span> bằng các <a href="/wiki/H%C3%A0m_s%C6%A1_c%E1%BA%A5p" class="mw-redirect" title="Hàm sơ cấp">hàm sơ cấp</a>, tuy nhiên <a href="/w/index.php?title=%C4%90%E1%BB%8Bnh_l%C3%BD_ngh%E1%BB%8Bch_%C4%91%E1%BA%A3o_Lagrange&action=edit&redlink=1" class="new" title="Định lý nghịch đảo Lagrange (trang không tồn tại)">định lý nghịch đảo Lagrange</a> cho ta nghiệm dưới dạng một <a href="/w/index.php?title=Chu%E1%BB%97i_l%C5%A9y_th%E1%BB%ABa&action=edit&redlink=1" class="new" title="Chuỗi lũy thừa (trang không tồn tại)">chuỗi lũy thừa</a> của <span class="texhtml mvar" style="font-style:italic;">e</span>:<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}E=M&+e\sin M+{\frac {e^{2}}{2}}\sin 2M\\+\ &{\frac {e^{3}}{3!\ 2^{2}}}\left(3^{2}\sin 3M-3\sin M\right)\\+\ &{\frac {e^{4}}{4!\ 2^{3}}}\left(4^{3}\sin 4M-4\cdot 2^{3}\sin 2M\right)\\+\ &{\frac {e^{3}}{5!\ 2^{4}}}\left(5^{4}\sin 5M-5\cdot 3^{4}\sin 3M+10\sin M\right)\\+\ &\cdots \end{aligned}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>E</mi> <mo>=</mo> <mi>M</mi> </mtd> <mtd> <mi></mi> <mo>+</mo> <mi>e</mi> <mi>sin</mi> <mo>⁡</mo> <mi>M</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mn>2</mn> </mfrac> </mrow> <mi>sin</mi> <mo>⁡</mo> <mn>2</mn> <mi>M</mi> </mtd> </mtr> <mtr> <mtd> <mo>+</mo> <mtext> </mtext> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow> <mn>3</mn> <mo>!</mo> <mtext> </mtext> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>sin</mi> <mo>⁡</mo> <mn>3</mn> <mi>M</mi> <mo>−</mo> <mn>3</mn> <mi>sin</mi> <mo>⁡</mo> <mi>M</mi> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>+</mo> <mtext> </mtext> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mrow> <mn>4</mn> <mo>!</mo> <mtext> </mtext> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <msup> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>sin</mi> <mo>⁡</mo> <mn>4</mn> <mi>M</mi> <mo>−</mo> <mn>4</mn> <mo>⋅</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>sin</mi> <mo>⁡</mo> <mn>2</mn> <mi>M</mi> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>+</mo> <mtext> </mtext> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow> <mn>5</mn> <mo>!</mo> <mtext> </mtext> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <msup> <mn>5</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>sin</mi> <mo>⁡</mo> <mn>5</mn> <mi>M</mi> <mo>−</mo> <mn>5</mn> <mo>⋅</mo> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>sin</mi> <mo>⁡</mo> <mn>3</mn> <mi>M</mi> <mo>+</mo> <mn>10</mn> <mi>sin</mi> <mo>⁡</mo> <mi>M</mi> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>+</mo> <mtext> </mtext> </mtd> <mtd> <mi></mi> <mo>⋯</mo> </mtd> </mtr> </mtable> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}E=M&+e\sin M+{\frac {e^{2}}{2}}\sin 2M\\+\ &{\frac {e^{3}}{3!\ 2^{2}}}\left(3^{2}\sin 3M-3\sin M\right)\\+\ &{\frac {e^{4}}{4!\ 2^{3}}}\left(4^{3}\sin 4M-4\cdot 2^{3}\sin 2M\right)\\+\ &{\frac {e^{3}}{5!\ 2^{4}}}\left(5^{4}\sin 5M-5\cdot 3^{4}\sin 3M+10\sin M\right)\\+\ &\cdots \end{aligned}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cbf4114324bd989612f7ceb82d5a9f3070462f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -13.171ex; width:52.496ex; height:27.509ex;" alt="{\displaystyle {\begin{aligned}E=M&+e\sin M+{\frac {e^{2}}{2}}\sin 2M\\+\ &{\frac {e^{3}}{3!\ 2^{2}}}\left(3^{2}\sin 3M-3\sin M\right)\\+\ &{\frac {e^{4}}{4!\ 2^{3}}}\left(4^{3}\sin 4M-4\cdot 2^{3}\sin 2M\right)\\+\ &{\frac {e^{3}}{5!\ 2^{4}}}\left(5^{4}\sin 5M-5\cdot 3^{4}\sin 3M+10\sin M\right)\\+\ &\cdots \end{aligned}}.}"></span></dd></dl> <p>Công thức tổng quát là:<sup id="cite_ref-const_2-0" class="reference"><a href="#cite_note-const-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=M+\sum _{n=1}^{\infty }{\frac {e^{n}}{2^{n-1}\,n!}}\sum _{k=0}^{\lfloor n/2\rfloor }(-1)^{k}\,{\binom {n}{k}}\,(n-2k)^{n-1}\,\sin((n-2k)\,M).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>M</mi> <mo>+</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mrow> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mi>n</mi> <mo>!</mo> </mrow> </mfrac> </mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo fence="false" stretchy="false">⌊</mo> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo fence="false" stretchy="false">⌋</mo> </mrow> </munderover> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mi>n</mi> <mi>k</mi> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> <mspace width="thinmathspace" /> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>2</mn> <mi>k</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>2</mn> <mi>k</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>M</mi> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=M+\sum _{n=1}^{\infty }{\frac {e^{n}}{2^{n-1}\,n!}}\sum _{k=0}^{\lfloor n/2\rfloor }(-1)^{k}\,{\binom {n}{k}}\,(n-2k)^{n-1}\,\sin((n-2k)\,M).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bdae8fcf4d4de562bd60a259ae785167e3f0610a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:66.651ex; height:7.843ex;" alt="{\displaystyle E=M+\sum _{n=1}^{\infty }{\frac {e^{n}}{2^{n-1}\,n!}}\sum _{k=0}^{\lfloor n/2\rfloor }(-1)^{k}\,{\binom {n}{k}}\,(n-2k)^{n-1}\,\sin((n-2k)\,M).}"></span></dd></dl> <p><a href="/wiki/Pierre-Simon_Laplace" title="Pierre-Simon Laplace">Laplace</a> nhận ra rằng chuỗi này hội tụ với <span class="texhtml mvar" style="font-style:italic;">e</span> bé, nhưng phân kỳ với mọi <span class="texhtml mvar" style="font-style:italic;">M</span> không phải là bội của <span class="texhtml">π</span> khi giá trị tâm sai <span class="texhtml mvar" style="font-style:italic;">e</span> vượt quá một hằng số nhất định, không phụ thuộc vào <span class="texhtml mvar" style="font-style:italic;">M</span>. Giá trị đó chính là giới hạn Laplace <span class="texhtml">λ</span>, và cũng là <a href="/w/index.php?title=B%C3%A1n_k%C3%ADnh_h%E1%BB%99i_t%E1%BB%A5&action=edit&redlink=1" class="new" title="Bán kính hội tụ (trang không tồn tại)">bán kính hội tụ</a> của chuỗi lũy thừa này. </p><p>Một biểu diễn khác là nếu ta gọi <span class="texhtml">μ = 1.1996786402…</span> là nghiệm dương của phương trình <span class="texhtml">coth <i>x</i> = <i>x</i></span> (trong đó <span class="texhtml">coth</span> là <a href="/wiki/H%C3%A0m_hyperbolic" class="mw-redirect" title="Hàm hyperbolic">hàm cotang hyperbolic</a>) thì <span class="texhtml">λ = <span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">μ<sup><small>2</small></sup> − 1</span></span></span>.<sup id="cite_ref-const_2-1" class="reference"><a href="#cite_note-const-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Từ đây có thể suy ra giá trị lớn nhất của hàm số <span class="texhtml"><i>x</i>/cosh <i>x</i></span> chính là <span class="texhtml">λ</span>, đạt tại <span class="texhtml"><i>x</i> = μ</span>. </p><p>Ngoài ra, <span class="texhtml">λ</span> là nghiệm dương duy nhất của phương trình </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {x\exp({\sqrt {1+x^{2}}})}{1+{\sqrt {1+x^{2}}}}}=1.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>x</mi> <mi>exp</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>+</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo stretchy="false">)</mo> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>+</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>1.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {x\exp({\sqrt {1+x^{2}}})}{1+{\sqrt {1+x^{2}}}}}=1.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b311dab7b894bbb53f7a5ecadda76a4dc1430844" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:21.533ex; height:7.509ex;" alt="{\displaystyle {\frac {x\exp({\sqrt {1+x^{2}}})}{1+{\sqrt {1+x^{2}}}}}=1.}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Xem_thêm"><span id="Xem_th.C3.AAm"></span>Xem thêm</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&veaction=edit&section=2" title="Sửa đổi phần “Xem thêm”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&action=edit&section=2" title="Sửa mã nguồn tại đề mục: Xem thêm"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%C4%90%E1%BB%99_l%E1%BB%87ch_t%C3%A2m_qu%E1%BB%B9_%C4%91%E1%BA%A1o" title="Độ lệch tâm quỹ đạo">Độ lệch tâm quỹ đạo</a></li> <li><a href="/w/index.php?title=Ph%C6%B0%C6%A1ng_tr%C3%ACnh_Kepler&action=edit&redlink=1" class="new" title="Phương trình Kepler (trang không tồn tại)">Phương trình Kepler</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Tham_khảo"><span id="Tham_kh.E1.BA.A3o"></span>Tham khảo</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&veaction=edit&section=3" title="Sửa đổi phần “Tham khảo”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&action=edit&section=3" title="Sửa mã nguồn tại đề mục: Tham khảo"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r71728118">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><b><a href="#cite_ref-1">^</a></b> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r67233549">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"“""”""‘""’"}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFMoulton1914" class="citation book cs1">Moulton, Forest R. (1914). “V. The Problem of Two Bodies”. <a rel="nofollow" class="external text" href="https://archive.org/details/introcelestial00moulrich"><i>An Introduction to Celestial Mechanics</i></a> (ấn bản thứ 2). MacMillan. tr. 169.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=V.+The+Problem+of+Two+Bodies&rft.btitle=An+Introduction+to+Celestial+Mechanics&rft.pages=169&rft.edition=2&rft.pub=MacMillan&rft.date=1914&rft.aulast=Moulton&rft.aufirst=Forest+R.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fintrocelestial00moulrich&rfr_id=info%3Asid%2Fvi.wikipedia.org%3AGi%E1%BB%9Bi+h%E1%BA%A1n+Laplace" class="Z3988"></span></span> </li> <li id="cite_note-const-2">^ <a href="#cite_ref-const_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-const_2-1"><sup><i><b>b</b></i></sup></a> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r67233549"><cite id="CITEREFFinch2003" class="citation book cs1">Finch, Steven (2003). <a rel="nofollow" class="external text" href="https://archive.org/details/mathematicalcons0000finc"><i>Mathematical constants</i></a>. <a href="/wiki/New_York" class="mw-redirect mw-disambig" title="New York">New York</a>: <a href="/wiki/Cambridge_University_Press" class="mw-redirect" title="Cambridge University Press">Cambridge University Press</a>. tr. <a rel="nofollow" class="external text" href="https://archive.org/details/mathematicalcons0000finc/page/267">267</a>. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Ngu%E1%BB%93n_s%C3%A1ch/978-0-521-81805-6" title="Đặc biệt:Nguồn sách/978-0-521-81805-6"><bdi>978-0-521-81805-6</bdi></a>. <a href="/wiki/OCLC_(%C4%91%E1%BB%8Bnh_danh)" class="mw-redirect" title="OCLC (định danh)">OCLC</a> <a rel="nofollow" class="external text" href="//www.worldcat.org/oclc/847526740">847526740</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematical+constants&rft.place=New+York&rft.pages=267&rft.pub=Cambridge+University+Press&rft.date=2003&rft_id=info%3Aoclcnum%2F847526740&rft.isbn=978-0-521-81805-6&rft.aulast=Finch&rft.aufirst=Steven&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmathematicalcons0000finc&rfr_id=info%3Asid%2Fvi.wikipedia.org%3AGi%E1%BB%9Bi+h%E1%BA%A1n+Laplace" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Liên_kết_ngoài"><span id="Li.C3.AAn_k.E1.BA.BFt_ngo.C3.A0i"></span>Liên kết ngoài</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&veaction=edit&section=4" title="Sửa đổi phần “Liên kết ngoài”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&action=edit&section=4" title="Sửa mã nguồn tại đề mục: Liên kết ngoài"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="citation mathworld" id="Reference-Mathworld-Laplace_Limit"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a>, "<a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/LaplaceLimit.html">Laplace Limit</a>" từ <a href="/wiki/MathWorld" title="MathWorld">MathWorld</a>.</span></li> <li>OEIS <a rel="nofollow" class="external text" href="https://oeis.org/A033259">dãy A033259</a> (Biểu diễn thập phân của hằng số giới hạn Laplace)</li></ul> <p><br /> </p> <div class="boilerplate metadata plainlinks" id="stub"><table class="metadata plainlinks stub" style="background: transparent;" role="presentation"><tbody><tr> <td><span typeof="mw:File"><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:S%C6%A1_khai_gi%E1%BA%A3i_t%C3%ADch_to%C3%A1n_h%E1%BB%8Dc" title="Thể loại:Sơ khai giải tích toán học"><img alt="Hình tượng sơ khai" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Lebesgue_Icon.svg/35px-Lebesgue_Icon.svg.png" decoding="async" width="35" height="35" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Lebesgue_Icon.svg/53px-Lebesgue_Icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Lebesgue_Icon.svg/70px-Lebesgue_Icon.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span></td> <td><i>Bài viết liên quan đến <a href="/wiki/Gi%E1%BA%A3i_t%C3%ADch_to%C3%A1n_h%E1%BB%8Dc" title="Giải tích toán học">giải tích toán học</a> này vẫn còn <a href="/wiki/Wikipedia:B%C3%A0i_s%C6%A1_khai" title="Wikipedia:Bài sơ khai">sơ khai</a>. Bạn có thể giúp Wikipedia <a class="external text" href="https://vi.wikipedia.org/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&veaction=edit">mở rộng nội dung</a> để bài được hoàn chỉnh hơn.</i><div class="plainlinks hlist navbar mini" style="position: absolute; right: 15px; display: none;"><ul><li class="nv-xem"><a href="/wiki/B%E1%BA%A3n_m%E1%BA%ABu:S%C6%A1_khai_gi%E1%BA%A3i_t%C3%ADch_to%C3%A1n_h%E1%BB%8Dc" title="Bản mẫu:Sơ khai giải tích toán học"><abbr title="Xem bản mẫu này">x</abbr></a></li><li class="nv-thảo luận"><a href="/w/index.php?title=Th%E1%BA%A3o_lu%E1%BA%ADn_B%E1%BA%A3n_m%E1%BA%ABu:S%C6%A1_khai_gi%E1%BA%A3i_t%C3%ADch_to%C3%A1n_h%E1%BB%8Dc&action=edit&redlink=1" class="new" title="Thảo luận Bản mẫu:Sơ khai giải tích toán học (trang không tồn tại)"><abbr title="Thảo luận bản mẫu này">t</abbr></a></li><li class="nv-sửa"><a class="external text" href="https://vi.wikipedia.org/w/index.php?title=B%E1%BA%A3n_m%E1%BA%ABu:S%C6%A1_khai_gi%E1%BA%A3i_t%C3%ADch_to%C3%A1n_h%E1%BB%8Dc&action=edit"><abbr title="Sửa bản mẫu này">s</abbr></a></li></ul></div></td> </tr></tbody></table></div> <div class="boilerplate metadata plainlinks" id="stub"><table class="metadata plainlinks stub" style="background: transparent;" role="presentation"><tbody><tr> <td><span typeof="mw:File"><a href="/wiki/T%E1%BA%ADp_tin:Science.jpg" class="mw-file-description"><img alt="Hình tượng sơ khai" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Science.jpg/30px-Science.jpg" decoding="async" width="30" height="32" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Science.jpg/45px-Science.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/54/Science.jpg/60px-Science.jpg 2x" data-file-width="70" data-file-height="75" /></a></span></td> <td><i>Bài viết về chủ đề <a href="/wiki/V%E1%BA%ADt_l%C3%BD_h%E1%BB%8Dc" title="Vật lý học">vật lý</a> này vẫn còn <a href="/wiki/Wikipedia:B%C3%A0i_s%C6%A1_khai" title="Wikipedia:Bài sơ khai">sơ khai</a>. Bạn có thể giúp Wikipedia <a class="external text" href="https://vi.wikipedia.org/w/index.php?title=Gi%E1%BB%9Bi_h%E1%BA%A1n_Laplace&veaction=edit">mở rộng nội dung</a> để bài được hoàn chỉnh hơn.</i><div class="plainlinks hlist navbar mini" style="position: absolute; right: 15px; display: none;"><ul><li class="nv-xem"><a href="/wiki/B%E1%BA%A3n_m%E1%BA%ABu:S%C6%A1_khai_v%E1%BA%ADt_l%C3%BD" title="Bản mẫu:Sơ khai vật lý"><abbr title="Xem bản mẫu này">x</abbr></a></li><li class="nv-thảo luận"><a href="/w/index.php?title=Th%E1%BA%A3o_lu%E1%BA%ADn_B%E1%BA%A3n_m%E1%BA%ABu:S%C6%A1_khai_v%E1%BA%ADt_l%C3%BD&action=edit&redlink=1" class="new" title="Thảo luận Bản mẫu:Sơ khai vật lý (trang không tồn tại)"><abbr title="Thảo luận bản mẫu này">t</abbr></a></li><li class="nv-sửa"><a class="external text" href="https://vi.wikipedia.org/w/index.php?title=B%E1%BA%A3n_m%E1%BA%ABu:S%C6%A1_khai_v%E1%BA%ADt_l%C3%BD&action=edit"><abbr title="Sửa bản mẫu này">s</abbr></a></li></ul></div></td> </tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Lấy từ “<a dir="ltr" href="https://vi.wikipedia.org/w/index.php?title=Giới_hạn_Laplace&oldid=69563934">https://vi.wikipedia.org/w/index.php?title=Giới_hạn_Laplace&oldid=69563934</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Th%E1%BB%83_lo%E1%BA%A1i" title="Đặc biệt:Thể loại">Thể loại</a>: <ul><li><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:Qu%E1%BB%B9_%C4%91%E1%BA%A1o" title="Thể loại:Quỹ đạo">Quỹ đạo</a></li><li><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:H%E1%BA%B1ng_s%E1%BB%91_to%C3%A1n_h%E1%BB%8Dc" title="Thể loại:Hằng số toán học">Hằng số toán học</a></li><li><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:Chu%E1%BB%97i_to%C3%A1n_h%E1%BB%8Dc" title="Thể loại:Chuỗi toán học">Chuỗi toán học</a></li><li><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:S%C6%A1_khai_gi%E1%BA%A3i_t%C3%ADch_to%C3%A1n_h%E1%BB%8Dc" title="Thể loại:Sơ khai giải tích toán học">Sơ khai giải tích toán học</a></li><li><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:S%C6%A1_khai_v%E1%BA%ADt_l%C3%BD" title="Thể loại:Sơ khai vật lý">Sơ khai vật lý</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Thể loại ẩn: <ul><li><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:T%E1%BA%A5t_c%E1%BA%A3_b%C3%A0i_vi%E1%BA%BFt_s%C6%A1_khai" title="Thể loại:Tất cả bài viết sơ khai">Tất cả bài viết sơ khai</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Trang này được sửa đổi lần cuối vào ngày 12 tháng 1 năm 2023, 15:53.</li> <li id="footer-info-copyright">Văn bản được phát hành theo <a href="/wiki/Wikipedia:Nguy%C3%AAn_v%C4%83n_Gi%E1%BA%A5y_ph%C3%A9p_Creative_Commons_Ghi_c%C3%B4ng%E2%80%93Chia_s%E1%BA%BB_t%C6%B0%C6%A1ng_t%E1%BB%B1_phi%C3%AAn_b%E1%BA%A3n_4.0_Qu%E1%BB%91c_t%E1%BA%BF" title="Wikipedia:Nguyên văn Giấy phép Creative Commons Ghi công–Chia sẻ tương tự phiên bản 4.0 Quốc tế">Giấy phép Creative Commons Ghi công–Chia sẻ tương tự</a>; có thể áp dụng điều khoản bổ sung. 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Giới hạn Laplace – Wikipedia tiếng Việt