This paper follows an earlier work [P. L. Butzer, C. Markett
and M. Schmidt
, Result. Math. 19, 257-274 (1991; Zbl 0724.11036
)] on Stirling numbers, central factorial numbers, and their relation to the values of the Riemann zeta function
, with special emphasis on the interaction between sum and integral identities. The principal results are new rapidly convergent series and integral representations for
and for special Dirichlet
-functions with integer argument.