by the method of weight coefficients, techniques of real analysis andhermite-hadamard's inequality, a half-discrete hardy-hilbert-type inequalityrelated to the kernel of the hyperbolic cosecant function with the best possibleconstant factor expressed in terms of the extended riemann-zeta function is proved.the more accurate equivalent forms, the operator expressions with the norm,the reverses a...

This paper investigates a generalization the classical Hurwitz zeta function. It is shown that many of the properties exhibited by this special function extends to class of functions called hypergeometric Hurwitz zeta functions, including their analytic continuation to the complex plane and a pre-functional equation satisfied by them. As an application, a formula for moments of hypergeometric H...

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Abstract. In this paper, we prove a new identity for values of the Hurwitz zeta function which contains as particular cases Koecher’s identity for odd zeta values, the Bailey-Borwein-Bradley identity for even zeta values and many other interesting formulas related to values of the Hurwitz zeta function. We also get an extension of the bivariate identity of Cohen to values of the Hurwitz zeta fu...

A number of authors have considered mean values of powers of the modulus of the Hurwitz zeta function ζ(s, a), see [3, 4, 5, 6, 7]. In this paper, the mean of the function itself is considered. First a functional equation relating the Riemann zeta function to sums of the values of the Hurwitz zeta function at rational values of a is derived. This functional equation underlies the vanishing of t...

We proved that the Hurwitz zeta function is prime. In addition, we derived Nevanlinna characteristic for this function.

In this paper, we further study the generating function involving a variety of special numbers and ploynomials constructed by second author. Applying Mellin transformation to function, define new class zeta type functions, which is related interpolation functions Apostol–Bernoulli polynomials, Bernoulli Euler polynomials. This Hurwitz alternating Lerch function. Furthermore, using these derive ...

Abstract: Motivated largely by a number of recent investigations, we introduce and investigate the various properties of a certain new family of the λ -generalized Hurwitz-Lerch zeta functions. We derive many potentially useful results involving these λ -generalized Hurwitz-Lerch zeta functions including (for example) their partial differential equations, new series and Mellin-Barnes type conto...

In this chapter, we will see a proof of the analytic continuation of the Riemann zeta function ζ(s) and the Dirichlet L function L(s, χ) via the Hurwitz zeta function. This then gives rise to a functional equation for ζ(s) and a direct computation for the value of this function at negative integer points. 1. The Hurwitz zeta function We have already seen the definition of the Riemann zeta funct...