Year: 2023
Type: preprint
Abstract: This paper presents a new approach to evaluating the special values of the Dirichlet beta function, $β(2k+1)$, where $k$ is any nonnegative integer. Our approach relies on some properties of the Euler numbers and polynomials, and uses basic calculus and telescoping series. By a similar procedure, we also yield an integral representation of $β(2k)$. The idea of our proof adapts from a previous study by Ciaurri et al., where the authors introduced a new proof of Euler's formula for $ζ(2k)$.
Source: arXiv (Cornell University)
Authors: Tanabe, Naomi, Wattanawanichkul, Nawapan
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Bowdoin College
OpenAlex ID: W4387074778