Elaboration of Some Results of Srivastava and Choi

Abstract

In this paper we shall utilize some recent results of %\cite{KKSY} S. Kanemitsu, H.\~Kumagai, H. M. Srivastava and M. Yoshimoto in {\it Appl. Math. Comput.} 154 (2004) %\cite{KKSY} on an asymptotic as well as an integral formula for the partial sum of the Hurwitz zeta-function, to elaborate on some results of Srivastava and Choi in {\it Series Associated with the Zeta and Related Functions} (Kluwer 2001), %\cite{SC}, and in some cases to give improved generalizations thereof. More specifically, we shall give an asymptotic expansion of the sum of the values derivative of the digamma function. We shall also re-establish Bendersky--Adamchik's result and Elizalde's result.