TY  - JOUR
T1  - PROBABILISTIC PROOF OF A SUMMATION FORMULA
AU  - Kım, Tae-kyun
AU  - Kim, Dae San
PY  - 2025
DA  - April
Y2  - 2025
DO  - 10.15672/hujms.1592384
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 1
EP  - 9
LA  - en
AB  - The aim of this paper is to derive a summation formula for the  series and an expression for ζ(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.
KW  - zeta function
KW  - hyperbolic secant random variable
KW  - moment generating function
KW  - robability density function
CR  - [1] J. A. Adell, B. Bényi, Probabilistic Stirling numbers and applications, Aequationes
Math. 98, no. 6, 1627-1646, 2024.
UR  - https://doi.org/10.15672/hujms.1592384
L1  - https://dergipark.org.tr/en/download/article-file/4398677
ER  -