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This is a Quantitative Study study.

September 16, 2025

Certain Integral Representation and Fractional Derivatives Associated to a General Function Related to Hurwitz-Lerch Zeta Function

Key Points

Established new integral representations related to a general function that unifies the Mittag-Leffler function.
Derived fractional derivatives and integrals involving the Hurwitz-Lerch Zeta function through the general function.
Evaluated specific integrals to demonstrate the relationship with the Mittag-Leffler function and its properties.
Applications of these findings can enhance the understanding of fractional calculus and its implications in mathematical physics.

Abstract

In this paper, some integral representation and fractional derivatives of a general function are established. The general function studied in this paper unifies the Mittag-Leffler function and the Hurwitz-Lerch Zeta function. We have evaluated certain type of integrals involving the Mittag-Leffler function which gives the general function as resultant. As application of these results the integral representation and fractional derivatives for simpler function related to the Hurwitz-Lerch Zeta function are shown to be derived.

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Certain Integral Representation and Fractional Derivatives Associated to a General Function Related to Hurwitz-Lerch Zeta Function

Key Points

Abstract

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