We consider a Hurwitz-Lerch zeta function Φ s , z a sum over the natural numbers. provide an analytically continued closed form solution for this in terms of addition functions. A new recurrence ...

The first published proof of key analytic properties of zeta-functions associated with quadratic forms is due to Paul Epstein [2] in 1903 (submitted January 1902). The corresponding name “Epstein zeta-functions” was introduced by Edward Charles Titchmarsh in his article [15] from 1934; soon after, this terminology became common through influential articles of Max Deuring and Carl Ludwig Siegel....

The aim of this paper is to investigate harmonic Stieltjes constants occurring in the Laurent expansions function \[ \zeta_{H}\left( s,a\right) =\sum_{n=0}^{\infty}\frac{1}{\left( n+a\right) ^{s}}\sum_{k=0}^{n}\frac{1}{k+a},\text{ }\operatorname{Re}\left( s\right) >1, \] which we call Hurwitz zeta function. In particular evaluation formulas for $\gamma_{H}\left( m,1/2\right) $ and m,1\right) ar...

ABSTRACT In the present paper we evaluate a general integral involving the product of the extension of the Hurwitz-Lerch Zeta function, product of two ,Bessel functions, multivariable Aleph-function Jacobi polynomial, the multivariable I-function defined by Prasad [4] and general class of polynomials of several variables. The importance of the result established in this paper lies in the fact t...