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Some series involving the zeta function. (English) Zbl 0830.11030

The knowledge of the double gamma function is applied in order to evaluate some series involving the Riemann zeta function and its generalization, the Hurwitz zeta function. The authors start their considerations from Alexeiwsky’s theorem concerning the integral of the logarithm of the ordinary gamma function (where the double gamma function appears in the result). They extend the theorem conveniently. After performing some analytical manipulations they obtain a series of formulas, some of which they compare with known ones. They finish with some considerations on the \(n\)-ple gamma functions and its uses in the computation of some determinants.

MSC:

11M06 \(\zeta (s)\) and \(L(s, \chi)\)
11M35 Hurwitz and Lerch zeta functions
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