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Series of sums of products of higher-order Bernoulli functions
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 functio...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer International Publishing
2017
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5597698/ https://www.ncbi.nlm.nih.gov/pubmed/28979083 http://dx.doi.org/10.1186/s13660-017-1494-9 |
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author | Kim, Taekyun Kim, Dae San Jang, Gwan-Woo Kwon, Jongkyum |
author_facet | Kim, Taekyun Kim, Dae San Jang, Gwan-Woo Kwon, Jongkyum |
author_sort | Kim, Taekyun |
collection | PubMed |
description | 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. |
format | Online Article Text |
id | pubmed-5597698 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2017 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-55976982017-10-02 Series of sums of products of higher-order Bernoulli functions Kim, Taekyun Kim, Dae San Jang, Gwan-Woo Kwon, Jongkyum J Inequal Appl Research 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. Springer International Publishing 2017-09-13 2017 /pmc/articles/PMC5597698/ /pubmed/28979083 http://dx.doi.org/10.1186/s13660-017-1494-9 Text en © The Author(s) 2017 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. |
spellingShingle | Research Kim, Taekyun Kim, Dae San Jang, Gwan-Woo Kwon, Jongkyum Series of sums of products of higher-order Bernoulli functions |
title | Series of sums of products of higher-order Bernoulli functions |
title_full | Series of sums of products of higher-order Bernoulli functions |
title_fullStr | Series of sums of products of higher-order Bernoulli functions |
title_full_unstemmed | Series of sums of products of higher-order Bernoulli functions |
title_short | Series of sums of products of higher-order Bernoulli functions |
title_sort | series of sums of products of higher-order bernoulli functions |
topic | Research |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5597698/ https://www.ncbi.nlm.nih.gov/pubmed/28979083 http://dx.doi.org/10.1186/s13660-017-1494-9 |
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