@article{article_1592384, title={An expression for zeta values and a summation formula via hyperbolic secant random variables}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={54}, pages={1897–1904}, year={2025}, DOI={10.15672/hujms.1592384}, author={Kım, Tae-kyun and Kim, Dae San}, keywords={Euler numbers; zeta function, hyperbolic secant random variable, moment generating function; probability density function}, 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.}, number={5}, publisher={Hacettepe University}