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Also, we give new interesting identities via the generating functions of Dirichlet's type of Eulerian polynomials. After, by applying Mellin transformation to this generating function of Dirichlet's type of Eulerian polynomials, we derive L-function for Eulerian polynomials which interpolates of Dirichlet's type of Eulerian polynomials at negative integers.","publication_date":"2014,,","publication_name":"Mathematical Sciences","grobid_abstract_attachment_id":"90519778"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"On the Dirichlet’s type of Eulerian polynomials","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [990498]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</script><script defer="" 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translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="1835750" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/1835750/New_Generalization_of_Eulerian_polynomials_and_Their_Application">New Generalization of Eulerian polynomials and Their Application</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="990498" href="https://hku-tr.academia.edu/saraci">Serkan Araci</a></div><p class="ds-related-work--metadata ds2-5-body-xs">J. Ana. Num. Theor. 2, No. 2, 59-63 (2014)</p><p class="ds-related-work--abstract ds2-5-body-sm">In the present paper, we introduce Eulerian polynomials with a and b parameters and give the definition of them. By using the definition of generating function for our polynomials, we derive some new identities in Theory of Analytic Numbers. Also, we give relations between Eulerian polynomials with a and b parameters, Bernstein polynomials, Poly-logarithm function, Bernoulli numbers and Euler numbers. 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Also we apply the method of analytic continuation of q-Euler polynomials which is the main result of this paper.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the families of q-Euler numbers and polynomials and their applications","attachmentId":33758441,"attachmentType":"pdf","work_url":"https://www.academia.edu/1230871/On_the_families_of_q_Euler_numbers_and_polynomials_and_their_applications","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/1230871/On_the_families_of_q_Euler_numbers_and_polynomials_and_their_applications"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="78718180" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/78718180/q_Euler_numbers_and_polynomials_associated_with_p_adic_q_integrals">q -Euler numbers and polynomials associated with p -adic q -integrals</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="39129151" href="https://independent.academia.edu/TaekyunKim3">Taekyun Kim</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Nonlinear Mathematical Physics, 2007</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"q -Euler numbers and polynomials associated with p -adic q -integrals","attachmentId":85667511,"attachmentType":"pdf","work_url":"https://www.academia.edu/78718180/q_Euler_numbers_and_polynomials_associated_with_p_adic_q_integrals","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/78718180/q_Euler_numbers_and_polynomials_associated_with_p_adic_q_integrals"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="68248378" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/68248378/New_Generalization_of_Eulerian_polynomials_and_their_applications">New Generalization of Eulerian polynomials and their applications</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="1105507" href="https://gantep.academia.edu/mehmetacikgoz">Mehmet Acikgoz</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv preprint arXiv:1208.1271, 2012</p><p class="ds-related-work--abstract ds2-5-body-sm">Abstract: In the present paper, we introduce Eulerian polynomials with a and b parameters and give the definition of them. By using the definition of generating function for our polynomials, we derive some new identities in Theory of Analytic Numbers. Also, we give relations between Eulerian polynomials with a and b parameters, Bernstein polynomials, Poly-logarithm function, Bernoulli numbers and Euler numbers. Moreover, we see that our polynomials at a=-1 are related to Euler-Zeta function at negative inetegers. Finally, we ...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"New Generalization of Eulerian polynomials and their applications","attachmentId":78792329,"attachmentType":"pdf","work_url":"https://www.academia.edu/68248378/New_Generalization_of_Eulerian_polynomials_and_their_applications","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/68248378/New_Generalization_of_Eulerian_polynomials_and_their_applications"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="91121866" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/91121866/New_Approach_to_q_Euler_Numbers_and_Polynomials">New Approach to q-Euler Numbers and Polynomials</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="26694576" href="https://independent.academia.edu/SeogHoonRim">Seog-Hoon Rim</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Advances in Difference Equations, 2010</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"New Approach to q-Euler Numbers and Polynomials","attachmentId":94498685,"attachmentType":"pdf","work_url":"https://www.academia.edu/91121866/New_Approach_to_q_Euler_Numbers_and_Polynomials","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/91121866/New_Approach_to_q_Euler_Numbers_and_Polynomials"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":90519778,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":90519778,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_90519778" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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data-collection-position="19" data-entity-id="65429769" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/65429769/_q_Bernoulli_Numbers_and_Polynomials_Associated_with_Multiple_q_Zeta_Functions_and_Basic_L_series">$q$-Bernoulli Numbers and Polynomials Associated with Multiple $q$-Zeta Functions and Basic $L$-series</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="146832572" href="https://independent.academia.edu/YilmazSimsek2">Yilmaz Simsek</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv: Number Theory, 2005</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"$q$-Bernoulli Numbers and Polynomials Associated with Multiple $q$-Zeta Functions and 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