Fourier series of higher-order Bernoulli functions and their applications

Fourier series of higher-order Bernoulli functions and their applications

In this paper, we study the Fourier series related to higher-order Bernoulli functions and give new identities for higher-order Bernoulli functions which are derived from the Fourier series of them.

Fourier series of higher-order Daehee and Changhee functions and their applications

In the paper, the author considers the Fourier series related to higher-order Daehee and Changhee functions and establishes some new identities for higher-order Daehee and Changhee functions.

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 functions given by sums of products of higher-order Bernoulli functions and derive their Fourier series ...

Fourier series of finite products of Bernoulli and Genocchi functions

In this paper, we consider three types of functions given by products of Bernoulli and Genocchi functions and derive some new identities arising from Fourier series expansions associated with Bernoulli and Genocchi functions. Furthermore, we will express each of them in terms of Bernoulli functions.

Higher-order Fourier Analysis and Applications