Some identities involving the central factorial numbers and Riemann zeta function.
For the central factorial numbers \(t(n, k)\) defined by the following generating function: \[ \Biggl[2\log\Biggl({z\over 2}+ \sqrt{1+{z^2\over 4}}\Biggr)\Biggr]^k= k! \sum^\infty_{n=k} t(n,k) {z^n\over n!}\qquad (z\in\mathbb{C};\,| z|< 1), \] the author derives several interesting summation identities which also involve the familiar zeta function of Riemann [see, for details, the reviewer and \textit{J. Choi}, Series associated with the zeta and related functions, Kluwer, Dordrecht (2001; Zbl 1014.33001)]. The results presented in this paper are much too involved to be reproduced here.
scientific article; zbMATH DE number 2076378