PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 62 (76), pp. 13--25 (1997)
On Mellin-Barnes type of integrals and sums associated with the Riemann zeta-function}
Masanori KatsuradaDepartment of Mathematics and Computer Science, Kagoshima University, Korimoto, Kagoshima 890, Japan
Abstract: Two types (binomial and exponential types) of power series, together with a related sum, associated with the Riemann zeta-function $\zeta(s)$ will be investigated by using Mellin-Barnes type integrals. As for generalizations of these sums we shall introduce hypergeometric type generating functions of $\zeta(s)$ and derive their basic properties.
Keywords: Riemann zeta-function, Hurwitz zeta-function, Mellin-Barnes integral, hypergeometric function
Classification (MSC2000): 11M06; 11M41
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