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      Series of sums of products of higher-order Bernoulli functions

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          Abstract

          It is shown in a previous work that Faber-Pandharipande-Zagier’s and Miki’s identities can be derived from a polynomial identity, which in turn follows from the Fourier series expansion of sums of products of Bernoulli functions. Motivated by and generalizing this, we consider three types of functions given by sums of products of higher-order Bernoulli functions and derive their Fourier series expansions. Moreover, we express each of them in terms of Bernoulli functions.

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          Hodge integrals and Gromov-Witten theory

          C. Faber, R. Pandharipande (2000)
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            Identities involving values of Bernstein, q-Bernoulli and q-Euler polynomials

            A. Bayad, T. Kim (2011)
            In this paper we give some relation involving values of q-Bernoulli, q-Euler and Bernstein polynomials. From these relations, we obtain some interesting identities on the q-Bernoulli, q-Euler and Bernstein polynomials.
            Article 0 comments Cited 31 times – based on 0 reviews
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              A relation between Bernoulli numbers

              Hiroo Miki (1978)
              Article 0 comments Cited 18 times – based on 0 reviews     Review now
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                Author and article information

                Contributors
                Taekyun Kim: tkkim@kw.ac.kr
                Dae San Kim: dskim@sogang.ac.kr
                Gwan-Woo Jang: jgw5687@naver.com
                Jongkyum Kwon: mathkjk26@gnu.ac.kr
                Journal
                Journal ID (nlm-ta): J Inequal Appl
                Journal ID (iso-abbrev): J Inequal Appl
                Title: Journal of Inequalities and Applications
                Publisher: Springer International Publishing (Cham )
                ISSN (Print): 1025-5834
                ISSN (Electronic): 1029-242X
                Publication date (Electronic): 13 September 2017
                Publication date PMC-release: 13 September 2017
                Publication date (Print): 2017
                Volume: 2017
                Issue: 1
                Electronic Location Identifier: 221
                Affiliations
                [1 ]GRID grid.410561.7, Department of Mathematics, College of Science, , Tianjin Polytechnic University, ; Tianjin, 300160 China
                [2 ]ISNI 0000 0004 0533 0009, GRID grid.411202.4, Department of Mathematics, , Kwangwoon University, ; Seoul, 139-701 Republic of Korea
                [3 ]ISNI 0000 0001 0286 5954, GRID grid.263736.5, Department of Mathematics, , Sogang University, ; Seoul, 121-742 Republic of Korea
                [4 ]ISNI 0000 0001 0661 1492, GRID grid.256681.e, Department of Mathematics Education and RINS, , Gyeongsang National University, ; Jinju, Gyeongsangnamdo 52828 Republic of Korea
                Article
                Publisher ID: 1494
                DOI: 10.1186/s13660-017-1494-9
                PMC ID: 5597698
                SO-VID: 8a350ffc-eff6-41dd-8720-2b3568b0699b
                Copyright © © The Author(s) 2017
                License:

                Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

                History
                Date received : 2 August 2017
                Date accepted : 31 August 2017
                Categories
                Subject: Research
                Custom metadata
                issue-copyright-statement © The Author(s) 2017

                Keywords: 11b68,42a16,fourier series,sums of products of higher-order bernoulli functions
                Data availability:
                Keywords: 11b68, 42a16, fourier series, sums of products of higher-order bernoulli functions

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