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Certain classes of series involving the zeta function. (English) Zbl 0932.11054
The authors apply the theory of the double Gamma function, which was recently revived in the study of the determinants of Laplacians, to evaluate some families of series involving the Riemann zeta-function. Introducing a (presumably new) mathematical constant in the theory of the double Gamma function, they also systematically evaluate a definite integral of the double Gamma function and various classes of series associated with Zeta functions. Some of these definite integrals are expressed in terms of quotients of double Gamma functions.
MSC:
 11M06 $\zeta \left(s\right)$ and $L\left(s,\chi \right)$ 33B99 Elementary classical functions