Abstract
The present paper aims at introducing and investigating a new class of generalized double zeta function i.e. modified double zeta function which involves the Riemann, Hurwitz, Hurwitz-Lerch, Barnes double zeta function and Bin-Saad generalized double zeta function as particular cases. The results are obtained by suitably applying Riemann-Liouville type and Tremblay fractional integral and differential operators. We derive the expansion formula for the proposed function with some of its properties via fractional operators and discuss the link with known results.
Highlights
Introduction and PreliminariesThe Hurwitz-Lerch zeta function [1] is defined by = ∅ ( y, z, a) ∑∞ yn n=0 (a + n)Z, a ∈ C \ {0, −1, −2, −3, }; y
The present paper aims at introducing and investigating a new kind of hypergeometric type function that is modified double zeta function via fractional calculus
In a sequel of result (5) here we introduce a modified double zeta function as follows ζ λμ,b=,c ( x, y; z, a)
Summary
The further generalization of Hurwitz-Lerch zeta function ∅ ( y, z, a) is defined by [2]. In [3] [4] Bin-Saad and Al-Gonah introduced two hypergeometric type generating functions of generalized zeta function as follows ζ. Rao [12] defined Wright type generalized hypergeometric function via fractional calculus. Many authors investigated the fractional calculus approach in study of generalized hypergeometric type function [13] [14]. The present paper aims at introducing and investigating a new kind of hypergeometric type function that is modified double zeta function via fractional calculus. Many Lemmas and particular cases have been discussed to relate known results
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