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Sums of certain series of the Riemann zeta function. (English) Zbl 0632.10040
The object of the present paper is to investigate systematically several interesting families of summation formulas involving finite series of the Riemann zeta-function. Many of the various results, which are unified (and generalized) here in a remarkably simple manner, have received considerable attention in recent years. We also present a brief account of a number of analogous results associated with the (Hurwitz’s) generalized zeta-function.

MSC:
11M06ζ(s) and L(s,χ)
11M35Hurwitz and Lerch zeta functions
33B15Gamma, beta and polygamma functions