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Elaboration of some results of Srivastava and Choi. (English) Zbl 1170.11322

Summary: In this paper we utilize some recent results of S. Kanemitsu, H. Kumagai, H. M. Srivastava and 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 H. M. Srivastava and 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.

MSC:

11M35 Hurwitz and Lerch zeta functions
33B15 Gamma, beta and polygamma functions
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References:

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