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...

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Bibliographic Details
Published in:Journal of inequalities and applications 2017, Vol.2017 (1), p.1-16, Article 221
Main Authors: Kim, Taekyun, Kim, Dae San, Jang, Gwan-Woo, Kwon, Jongkyum
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Fourier series
Functions (mathematics)
Mathematical analysis
Mathematics
Mathematics and Statistics
Series expansion
Sums
sums of products of higher-order Bernoulli functions
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Summary: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.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-017-1494-9