Abstract
AbstractThe goal of the paper is twofold. First, we present an analytic method leading to a class of combinatorial identities with Bernoulli, Euler and Catalan numbers based on considering specific multiple zeta-like series and infinite products. The developed method allows us to naturally extend Hoffman’s combinatorial identity that led to the famous evaluation of the multiple zeta value $$\zeta (\{2\}_k)$$
ζ
(
{
2
}
k
)
in 1992. Second, we present new evaluations of two multiple zeta-like series with their consequences to combinatorial identities, and, as a by-product of our technical considerations, we establish two combinatorial identities with a trinomial coefficient and Stirling numbers respectively.
Funder
Technical University of Ostrava
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Mathematics (miscellaneous)
Reference16 articles.
1. Burgos Gil, J.I., Fresán, J.: Multiple zeta values: from numbers to motives (2020). https://javier.fresan.perso.math.cnrs.fr/mzv.pdf
2. Chen, K.-W., Chung, C.-L.: Sum relations of multiple zeta star values with even arguments. Mediterr. J. Math. 14(3), 1–13 (2017)
3. Chen, K.-W., Chung, C.-L., Eie, M.: Sum formulas of multiple zeta values with arguments multiples of a common positive integer. J. Number Theory 177, 479–496 (2017)
4. Chen, X.-Y., Wu, L., Lim, D., Qi, F.: Two identities and closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of the second kind. Demonstr. Math. 55, 822–830 (2022)
5. Eie, M.: The Theory of Multiple Zeta Values with Applications in Combinatorics. World Scientific, Singapore (2013)