Sums of finite products of Genocchi functions

Advances in Difference Equations

Dae San Kim¹  Taekyun Kim²  Lee Chae Jang³  Gwan-Woo Jang⁴ 

[1] Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin, China;Department of Mathematics, Kwangwoon University, Seoul, Republic of Korea;Department of Mathematics, Sogang University, Seoul, Republic of Korea;Graduate School of Education, Konkuk University, Seoul, Republic of Korea

关键词: Fourier series;    Bernoulli functions;    Genocchi polynomials;    Genocchi functions;    11B83;    42A16;   

DOI  :  10.1186/s13662-017-1325-9

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In a previous work, it was shown that Faber-Pandharipande-Zagier and Miki’s identities can be derived from a polynomial identity which in turn follows from a Fourier series expansion of sums of products of Bernoulli functions. Motivated by this work, we consider three types of sums of finite products of Genocchi functions and derive Fourier series expansions for them. Moreover, we will be able to express each of them in terms of Bernoulli functions.

【 授权许可】

CC BY