Abstract
2010 Mathematics Subject ClassificationPrimary 11M25, 33C60; Secondary 33C05
Highlights
We show the hitherto unnoticed fact that the so-called τ -generalized Riemann Zeta function, which happens to be the main subject of investigation by Gupta and Kumari (2011) and by Saxena et al (2011a), is a seemingly trivial notational variation of the familiar general
The Eulerian Gamma-function integrals involving the generating functions λ(z, t; s, a) and (z, t; s, a) defined by (3.2) and (3.3), respectively, which are asserted by Theorem 4 below, can be evaluated by applying the wellknown formula (3.13)
In terms of the sequence { n}n∈N0 of the coefficients given by the definition (2.13), each of the following single or double Eulerian Gamma-function integral formulas holds true: 1 (μ) tμ−1 e−κt λ z, ωe−δt; s, a dt
Summary
We present a sum-integral representation formula for the general family of the extended Hurwitz-Lerch Zeta functions. The following straightforward generalization of the sum-integral representation (2.1) involving the familiar general Hurwitz-Lerch Zeta function (z, s, a) defined by (1.1) was given by Lin and Srivastava
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