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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... Full description

Journal Title: Journal of Inequalities and Applications 2017, Vol.2017(1), pp.1-16
Main Author: Kim, Taekyun
Other Authors: Kim, Dae , Jang, Gwan-Woo , Kwon, Jongkyum
Format: Electronic Article Electronic Article
Language: English
Subjects:
ID: E-ISSN: 1029-242X ; DOI: 10.1186/s13660-017-1494-9
Zum Text:
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recordid: springer_jour10.1186/s13660-017-1494-9
title: Series of sums of products of higher-order Bernoulli functions
format: Article
creator:
  • Kim, Taekyun
  • Kim, Dae
  • Jang, Gwan-Woo
  • Kwon, Jongkyum
subjects:
  • Fourier series
  • sums of products of higher-order Bernoulli functions
ispartof: Journal of Inequalities and Applications, 2017, Vol.2017(1), pp.1-16
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.
language: eng
source:
identifier: E-ISSN: 1029-242X ; DOI: 10.1186/s13660-017-1494-9
fulltext: fulltext_linktorsrc
issn:
  • 1029-242X
  • 1029242X
url: Link


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subjectFourier series ; sums of products of higher-order Bernoulli functions
descriptionIt 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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descriptionIt 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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abstractIt 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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