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Thomas John I'Anson Bromwich - Wikipedia

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</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">From Wikipedia, the free encyclopedia</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="en" dir="ltr"><p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Thomas John I'Anson Bromwich</div><div class="honorific-suffix" style="font-size: 77%; font-weight: normal;"><span class="nobold noexcerpt nowraplinks" style="font-size:;"><span style="font-size: 100%;"><a href="/wiki/Fellow_of_the_Royal_Society" title="Fellow of the Royal Society">FRS</a></span></span></div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Thomas_John_Bromwich.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Thomas_John_Bromwich.jpg/220px-Thomas_John_Bromwich.jpg" decoding="async" width="220" height="268" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/d/de/Thomas_John_Bromwich.jpg 1.5x" data-file-width="268" data-file-height="326" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><span style="display:none">(<span class="bday">1875-02-08</span>)</span>8 February 1875<br /><div style="display:inline" class="birthplace"><a href="/wiki/Wolverhampton" title="Wolverhampton">Wolverhampton</a>, <a href="/wiki/Staffordshire" title="Staffordshire">Staffordshire</a>, England</div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">24 August 1929<span style="display:none">(1929-08-24)</span> (aged&#160;54)<br /><div style="display:inline" class="deathplace"><a href="/wiki/Northampton" title="Northampton">Northampton</a>, <a href="/wiki/Northamptonshire" title="Northamptonshire">Northamptonshire</a>, England</div></td></tr><tr><th scope="row" class="infobox-label">Alma&#160;mater</th><td class="infobox-data"><a href="/wiki/St_John%27s_College,_Cambridge" title="St John&#39;s College, Cambridge">St John's College</a>, <a href="/wiki/University_of_Cambridge" title="University of Cambridge">Cambridge</a></td></tr></tbody></table> <p><b>Thomas John I'Anson Bromwich</b> <span class="nobold noexcerpt nowraplinks" style="font-size:;"><span style="font-size: 85%;"><a href="/wiki/Fellow_of_the_Royal_Society" title="Fellow of the Royal Society">FRS</a></span></span> (8 February 1875 – 24 August 1929) was an <a href="/wiki/English_people" title="English people">English</a> <a href="/wiki/Mathematician" title="Mathematician">mathematician</a>, and a Fellow of the <a href="/wiki/Royal_Society" title="Royal Society">Royal Society</a>.<sup id="cite_ref-Hardy1929a_1-0" class="reference"><a href="#cite_note-Hardy1929a-1"><span class="cite-bracket">&#91;</span>1<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">&#91;</span>2<span class="cite-bracket">&#93;</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Life">Life</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thomas_John_I%27Anson_Bromwich&amp;action=edit&amp;section=1" title="Edit section: Life"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Thomas John I'Anson Bromwich was born on 8 February 1875, in <a href="/wiki/Wolverhampton" title="Wolverhampton">Wolverhampton</a>, England. He was descended from Bryan I'Anson, of <a href="/wiki/Ashby_St_Ledgers" title="Ashby St Ledgers">Ashby St Ledgers</a>, Sheriff of London and father of the 17th century 1st Baronet Sir Bryan I'Anson of Bassetsbury. </p><p>His parents emigrated to <a href="/wiki/South_Africa" title="South Africa">South Africa</a>, where in 1892 he graduated from high school. He attended <a href="/wiki/St_John%27s_College,_Cambridge" title="St John&#39;s College, Cambridge">St John's College, Cambridge</a>, where in 1895 he became <a href="/wiki/Senior_Wrangler" title="Senior Wrangler">Senior Wrangler</a>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">&#91;</span>3<span class="cite-bracket">&#93;</span></a></sup> In 1897, he became a lecturer at St. John’s. From 1902 to 1907, he was a professor of mathematics at <a href="/wiki/National_University_of_Ireland,_Galway" class="mw-redirect" title="National University of Ireland, Galway">Queen’s College, Galway</a>. In 1906, he was elected a <a href="/wiki/Fellow_of_the_Royal_Society" title="Fellow of the Royal Society">Fellow of the Royal Society</a>. In 1907, he returned to Cambridge and again became a Fellow and lecturer at St. John’s. He was a vice president of the Royal Society in 1919 and 1920. He died in <a href="/wiki/Northampton" title="Northampton">Northampton</a> on 24 August 1929, hanging himself in his bedroom.<sup id="cite_ref-Hardy1929a_1-1" class="reference"><a href="#cite_note-Hardy1929a-1"><span class="cite-bracket">&#91;</span>1<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">&#91;</span>4<span class="cite-bracket">&#93;</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Work">Work</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thomas_John_I%27Anson_Bromwich&amp;action=edit&amp;section=2" title="Edit section: Work"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Bromwich worked in both <a href="/wiki/Algebra" title="Algebra">algebra</a> and <a href="/wiki/Analysis" title="Analysis">analysis</a>. <a href="/wiki/G._H._Hardy" title="G. H. Hardy">G. H. Hardy</a> called him "The best pure mathematician among the applied mathematicians at Cambridge, and the best applied mathematician among the pure mathematicians".<sup id="cite_ref-Hardy1929a_1-2" class="reference"><a href="#cite_note-Hardy1929a-1"><span class="cite-bracket">&#91;</span>1<span class="cite-bracket">&#93;</span></a></sup> </p><p>Today, Bromwich is perhaps best known for justifying <a href="/wiki/Oliver_Heaviside" title="Oliver Heaviside">Oliver Heaviside</a>'s operator calculus.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">&#91;</span>5<span class="cite-bracket">&#93;</span></a></sup> Part of this involved using a <a href="/wiki/Contour_integral" class="mw-redirect" title="Contour integral">contour integral</a> to do an <a href="/wiki/Inverse_Laplace_transform" title="Inverse Laplace transform">inverse Laplace transform</a>. This particular contour integral is now often called the <i>Bromwich integral</i>, although it is also called by other names. </p><p>Other topics Bromwich investigated include solutions of the <a href="/wiki/Maxwell%27s_equations" title="Maxwell&#39;s equations">Maxwell's equations</a>, and the scattering of electromagnetic <a href="/wiki/Plane_wave" title="Plane wave">plane waves</a> by spheres. He also investigated, and wrote a book on, the theory of <a href="/wiki/Quadratic_form" title="Quadratic form">quadratic forms</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">&#91;</span>6<span class="cite-bracket">&#93;</span></a></sup> </p><p>In 1906 he derived <a href="/w/index.php?title=Bromwich_inequality&amp;action=edit&amp;redlink=1" class="new" title="Bromwich inequality (page does not exist)">Bromwich inequality</a> in the field of <a href="/wiki/Matrix_(mathematics)" title="Matrix (mathematics)">matrices</a> which gives narrower bounds to characteristic roots than those given by <a href="/wiki/Bendixson%27s_inequality" title="Bendixson&#39;s inequality">Bendixson's inequality</a>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">&#91;</span>7<span class="cite-bracket">&#93;</span></a></sup> </p><p>In 1908 he wrote <i>An introduction to the theory of infinite series</i>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">&#91;</span>8<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">&#91;</span>9<span class="cite-bracket">&#93;</span></a></sup> A second edition appeared in 1926. G. H. Hardy praised the book highly, while criticizing the way in which it was laid out.<sup id="cite_ref-Hardy1929a_1-3" class="reference"><a href="#cite_note-Hardy1929a-1"><span class="cite-bracket">&#91;</span>1<span class="cite-bracket">&#93;</span></a></sup> The book is still in print.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">&#91;</span>10<span class="cite-bracket">&#93;</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thomas_John_I%27Anson_Bromwich&amp;action=edit&amp;section=3" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.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"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Hardy1929a-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Hardy1929a_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Hardy1929a_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Hardy1929a_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Hardy1929a_1-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background: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.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFHardy1930" class="citation journal cs1"><a href="/wiki/G._H._Hardy" title="G. H. Hardy">Hardy, G. H.</a> (1930). "Thomas John I'Anson Bromwich". <i>Journal of the London Mathematical Society</i>. <b>5</b> (3): 209–220. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1112%2Fjlms%2Fs1-5.3.209">10.1112/jlms/s1-5.3.209</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Journal+of+the+London+Mathematical+Society&amp;rft.atitle=Thomas+John+I%27Anson+Bromwich&amp;rft.volume=5&amp;rft.issue=3&amp;rft.pages=209-220&amp;rft.date=1930&amp;rft_id=info%3Adoi%2F10.1112%2Fjlms%2Fs1-5.3.209&amp;rft.aulast=Hardy&amp;rft.aufirst=G.+H.&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AThomas+John+I%27Anson+Bromwich" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">His third name begins with an uppercase i, as opposed to a lowercase L.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFACADBRMC892TJ" class="citation encyclopaedia cs1"><a rel="nofollow" class="external text" href="http://venn.lib.cam.ac.uk/cgi-bin/search-2018.pl?sur=&amp;suro=w&amp;fir=&amp;firo=c&amp;cit=&amp;cito=c&amp;c=all&amp;z=all&amp;tex=BRMC892TJ&amp;sye=&amp;eye=&amp;col=all&amp;maxcount=50">"Bromwich, Thomas John I'Anson (BRMC892TJ)"</a>. <i>A Cambridge Alumni Database</i>. University of Cambridge.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=bookitem&amp;rft.atitle=Bromwich%2C+Thomas+John+I%27Anson+%28BRMC892TJ%29&amp;rft.btitle=A+Cambridge+Alumni+Database&amp;rft.pub=University+of+Cambridge&amp;rft_id=http%3A%2F%2Fvenn.lib.cam.ac.uk%2Fcgi-bin%2Fsearch-2018.pl%3Fsur%3D%26suro%3Dw%26fir%3D%26firo%3Dc%26cit%3D%26cito%3Dc%26c%3Dall%26z%3Dall%26tex%3DBRMC892TJ%26sye%3D%26eye%3D%26col%3Dall%26maxcount%3D50&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AThomas+John+I%27Anson+Bromwich" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://newspapers.com/article/saffron-walden-weekly-news/134058895/">"Cambridge Scholar's Suicide"</a>. <i>Saffron Walden Weekly News</i>. 30 August 1929. p.&#160;7<span class="reference-accessdate">. Retrieved <span class="nowrap">25 October</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Saffron+Walden+Weekly+News&amp;rft.atitle=Cambridge+Scholar%27s+Suicide&amp;rft.pages=7&amp;rft.date=1929-08-30&amp;rft_id=https%3A%2F%2Fnewspapers.com%2Farticle%2Fsaffron-walden-weekly-news%2F134058895%2F&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AThomas+John+I%27Anson+Bromwich" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJeffreys1929" class="citation journal cs1">Jeffreys, Harold (1929). "Bromwich's Work on Operational Methods". <i>Journal of the London Mathematical Society</i>. <b>3</b> (3): 220–223. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1112%2Fjlms%2Fs1-5.3.220">10.1112/jlms/s1-5.3.220</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Journal+of+the+London+Mathematical+Society&amp;rft.atitle=Bromwich%27s+Work+on+Operational+Methods&amp;rft.volume=3&amp;rft.issue=3&amp;rft.pages=220-223&amp;rft.date=1929&amp;rft_id=info%3Adoi%2F10.1112%2Fjlms%2Fs1-5.3.220&amp;rft.aulast=Jeffreys&amp;rft.aufirst=Harold&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AThomas+John+I%27Anson+Bromwich" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBôcher1908" class="citation journal cs1"><a href="/wiki/Maxime_B%C3%B4cher" title="Maxime Bôcher">Bôcher, Maxime</a> (1908). <a rel="nofollow" class="external text" href="http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&amp;id=pdf_1&amp;handle=euclid.bams/1183419616">"Review: T. J. I' A. Bromwich, Quadratic Forms and their Classification by Means of Invariant Factors"</a>. <i><a href="/wiki/Bulletin_of_the_American_Mathematical_Society" title="Bulletin of the American Mathematical Society">Bulletin of the American Mathematical Society</a></i>. <b>14</b> (4): 194–195. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1090%2FS0002-9904-1908-01579-9">10.1090/S0002-9904-1908-01579-9</a></span><span class="reference-accessdate">. Retrieved <span class="nowrap">4 December</span> 2008</span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Bulletin+of+the+American+Mathematical+Society&amp;rft.atitle=Review%3A+T.+J.+I%27+A.+Bromwich%2C+Quadratic+Forms+and+their+Classification+by+Means+of+Invariant+Factors&amp;rft.volume=14&amp;rft.issue=4&amp;rft.pages=194-195&amp;rft.date=1908&amp;rft_id=info%3Adoi%2F10.1090%2FS0002-9904-1908-01579-9&amp;rft.aulast=B%C3%B4cher&amp;rft.aufirst=Maxime&amp;rft_id=http%3A%2F%2Fprojecteuclid.org%2FDPubS%2FRepository%2F1.0%2FDisseminate%3Fview%3Dbody%26id%3Dpdf_1%26handle%3Deuclid.bams%2F1183419616&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AThomas+John+I%27Anson+Bromwich" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMirsky2012" class="citation book cs1">Mirsky, L. (3 December 2012). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=TteOFYtbIVQC"><i>An Introduction to Linear Algebra</i></a>. p.&#160;388. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a>&#160;<a href="/wiki/Special:BookSources/9780486166445" title="Special:BookSources/9780486166445"><bdi>9780486166445</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">16 October</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=An+Introduction+to+Linear+Algebra&amp;rft.pages=388&amp;rft.date=2012-12-03&amp;rft.isbn=9780486166445&amp;rft.aulast=Mirsky&amp;rft.aufirst=L.&amp;rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DTteOFYtbIVQC&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AThomas+John+I%27Anson+Bromwich" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=Cik6AQAAMAAJ&amp;pg=PA242">"Review: <i>An Introduction to the Theory of Infinite Series</i>"</a>. <i>Nature</i>. <b>78</b> (2020): 242. 16 July 1908. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F078242a0">10.1038/078242a0</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/2027%2Fmdp.39015064521290">2027/mdp.39015064521290</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a>&#160;<a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4047600">4047600</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Nature&amp;rft.atitle=Review%3A+An+Introduction+to+the+Theory+of+Infinite+Series&amp;rft.volume=78&amp;rft.issue=2020&amp;rft.pages=242&amp;rft.date=1908-07-16&amp;rft_id=info%3Ahdl%2F2027%2Fmdp.39015064521290&amp;rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4047600%23id-name%3DS2CID&amp;rft_id=info%3Adoi%2F10.1038%2F078242a0&amp;rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DCik6AQAAMAAJ%26pg%3DPA242&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AThomas+John+I%27Anson+Bromwich" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBromwich1908" class="citation journal cs1">Bromwich, Thomas John I'Anson (1908). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=NmVbAAAAcAAJ">"An Introduction to the Theory of Infinite Series (First edition)"</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.atitle=An+Introduction+to+the+Theory+of+Infinite+Series+%28First+edition%29&amp;rft.date=1908&amp;rft.aulast=Bromwich&amp;rft.aufirst=Thomas+John+I%27Anson&amp;rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DNmVbAAAAcAAJ&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AThomas+John+I%27Anson+Bromwich" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_journal" title="Template:Cite journal">cite journal</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Cite journal requires <code class="cs1-code">&#124;journal=</code> (<a href="/wiki/Help:CS1_errors#missing_periodical" title="Help:CS1 errors">help</a>)</span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBromwich1926" class="citation book cs1">Bromwich, Thomas John I'Anson (1926). <i>An introduction to the theory of infinite series</i>. American Mathematical Society Chelsea Publishing. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a>&#160;<a href="/wiki/Special:BookSources/978-0-8284-0335-1" title="Special:BookSources/978-0-8284-0335-1"><bdi>978-0-8284-0335-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=An+introduction+to+the+theory+of+infinite+series&amp;rft.pub=American+Mathematical+Society+Chelsea+Publishing&amp;rft.date=1926&amp;rft.isbn=978-0-8284-0335-1&amp;rft.aulast=Bromwich&amp;rft.aufirst=Thomas+John+I%27Anson&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AThomas+John+I%27Anson+Bromwich" class="Z3988"></span> Here is the <a rel="nofollow" class="external text" href="http://www.ams.org/bookstore?s3=bromwich&amp;pg1=&amp;s1=&amp;op1=AND&amp;co1=AND&amp;pg2=&amp;s2=&amp;op2=AND&amp;co2=AND&amp;op3=AND&amp;co3=AND&amp;pg3=ALLF&amp;fn=100&amp;d=BOOK&amp;p=1&amp;u=&amp;r=0&amp;l=100&amp;f=S&amp;subject=genint">publisher's description</a></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thomas_John_I%27Anson_Bromwich&amp;action=edit&amp;section=4" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO&#39;ConnorRobertson" class="citation cs2">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Bromwich.html">"Thomas John I&#39;Anson Bromwich"</a>, <i><a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a></i>, <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a><span class="reference-accessdate">, retrieved <span class="nowrap">5 December</span> 2008</span></cite><span 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