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Zbl 0830.11030
Choi, Junesang; Srivastava, H.M.; Quine, J.R.
Some series involving the zeta function. (English)
[J] Bull. Aust. Math. Soc. 51, No.3, 383-393 (1995). ISSN 0004-9727

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.
[E.Elizalde (Barcelona)]

MSC 2000:: *11M06 Riemannian zeta-function and Dirichlet L-function
11M35 Other zeta functions

Keywords: double gamma function; series involving the Riemann zeta function; Hurwitz zeta function

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