On extended Hurwitz-Lerch zeta function

This paper investigates an extended form of a beta function B-p,B-q (x, y). We first study the convergence problem of the function B-p,B-q (x, y) and consider the completely monotonic and log-convex properties of this function. As a result, we obtain a pair of Laguerre type inequalities. Next, we provide a new double integral representation for the function B-p,B-q (x, y). Subsequently, we consider the convergence problem of the extended Hurwitz-Lerch zeta function Phi(lambda,mu;v) (z, s, a; p, q) defined by its series representation. Upon using the series manipulation techniques, we obtain two series identities. We also find various integral representations for the function. Phi(lambda,mu;v) (z, s, a; p, q). Lastly, we apply Fourier analysis to the function z(a) Phi(mu;v) (z, s, a; p, q) and obtain a Lindelof-Wirtinger type expansion. Some interesting and promising results are also illustrated. (C) 2016 Elsevier Inc. All rights reserved.