The Stieltjes constants γk(a) are the expansion coefficients in the Laurent series for the Hurwitz zeta function about s = 1. We present new asymptotic, summatory, and other exact expressions for these and related constants.

The properties of the universal Bernoulli polynomials are illustrated and a new class of related L-functions is constructed. A generalization of the Riemann-Hurwitz zeta function is also proposed. Mathematics Subject Classification (2010): 11M41 (primary); 55N22 (secondary).

In the present paper certain subclasses of strongly starlike and strongly convex functions defined by convolution with the generalized Hurwitz -Lerch Zeta function are investigated. Some inclusion relations are also mentioned as special cases of our main results.

In the paper, we construct an absolutely convergent Dirichlet series which in mean is close to periodic Hurwitz zeta-function, and has universality property on approximation of a wide class analytic functions.

We present analytic properties and extensions of the constants ck appearing in the Báez-Duarte criterion for the Riemann hypothesis. These constants are the coefficients of Pochhammer polynomials in a series representation of the reciprocal of the Riemann zeta function. We present generalizations of this representation to the Hurwitz zeta and many other special functions. We relate the correspo...

This paper studies algebraic and analytic structures associated with the Lerch zeta function. It defines a family of two-variable Hecke operators {Tm : m ≥ 1} given by Tm(f )(a, c) = 1 m ∑m−1 k=0 f ( a+k m ,mc) acting on certain spaces of real-analytic functions, including Lerch zeta functions for various parameter values. The actions of various related operators on these function spaces are de...

We apply our simultaneous contour integral method to an infinite sum in Prudnikov et al. and use it derive the of Incomplete gamma function terms Hurwitz zeta function. then evaluate this formula new series special functions fundamental constants. All results work are new.

Abstract In this article, we give another method to calculate the values of multiple Hurwitz zeta function at non-positive integers by means Raabe ’s formula and Bernoulli numbers simplify these symbolic computation techniques.