An expression for zeta values and a summation formula via hyperbolic secant random variables
Year: 2025
Type: article
Abstract: The aim of this paper is to derive a summation formula for the series $\sum_{k=0}^{\infty} \frac{(-1)^{k}} {(2k+1)^{2n+1}}$ and an expression for $\zeta(2n+2)$ by using hyperbolic secant random variables. These identities involve Euler numbers and are obtained by computing the moments of the random variable and the moments of the sum of two independent such random variables.
Authors: Tae-kyun Kım, Dae San Kim
Institutions: Kwangwoon University, Sogang University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409371066