Recently, Special Function Theory (SPFT) and Operator (OPT) have acquired a lot of concern due to their considerable applications in disciplines pure applied mathematics. The Hurwitz-Lerch Zeta type functions, as part (SPFT), are significant developing providing further new studies. In complex domain, the convolution tool is salutary technique for systematic analytical characterization geometri...

By means of the Hadamard product, the present paper introduces new classes, Σ t, * a (α, β, ρ) and Σ t a (α, β, ρ) of Hurwitz-Lerch-Zeta function in the punctured disk U * = {z : 0 < |z| < 1}. In addition, the study investigates a number of inclusion relationships, properties and derives some interesting properties depending on some integral properties.

Abstract. In this paper we present a simple method for deriving recurrence relations and we apply it to obtain two equations involving the Lerch Phi function and sums of Bernoulli and Euler polynomials. Connections between these results and those obtained by H.M. Srivastava, M.L. Glasser and V. Adamchik ([8]) are pointed out, emphasizing the usefulness of this approach with some meaningful exam...

We derive new reduction formulas for the incomplete beta function B?,0,z and Lerch transcendent ?z,1,? in terms of elementary functions when ? is rational z complex. As an application, we calculate some integrals. Additionally, use these to test performance algorithms devoted numerical evaluation function.

The present work is a sequel to the papers [3] and [4], and it aims at introducing and investigating a new generalized double zeta function involving the Riemann, Hurwitz, Hurwitz-Lerch and Barnes double zeta functions as particular cases. We study its properties, integral representations, differential relations, series expansion and discuss the link with known results.