Elaboration of some results of Srivastava and Choi (Q873758)

Summary: In this paper we utilize some recent results of \textit{S. Kanemitsu, H.~Kumagai, H. M. Srivastava} and \textit{M. Yoshimoto} in [Appl. Math. Comput. 154, No. 3, 641--664 (2004; Zbl 1130.11049)] on an asymptotic as well as an integral formula for the partial sum of the Hurwitz zeta-function, to elaborate on some results of \textit{H.~M.~Srivastava} and \textit{J. Choi} [Series associated with the zeta and related functions. Dordrecht: Kluwer Academic Publishers (2001; Zbl 1014.33001)], and in some cases to give improved generalizations thereof. More specifically, we give an asymptotic expansion of the sum of the values derivative of the digamma function. We also re-establish Bendersky-Adamchik's result and Elizalde's result.