FURTHER EXPANSION FORMULAS FOR A CLASS OF GENERALIZED HURWITZ-LERCH ZETA FUNCTIONS OBTAINED BY MEANS OF A NEW LEIBNIZ RULE FOR FRACTIONAL DERIVATIVES - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

FURTHER EXPANSION FORMULAS FOR A CLASS OF GENERALIZED HURWITZ-LERCH ZETA FUNCTIONS OBTAINED BY MEANS OF A NEW LEIBNIZ RULE FOR FRACTIONAL DERIVATIVES

Résumé

The aim of this paper is to make use of a new generalized Leibniz rule for fractional derivatives obtained recently by Tremblay et al. [Tremblay, Gaboury and Fugère, A new Leibniz rule and its integral analogue for fractional derivatives, Integral Transforms Spec. Funct. 24 (2013), 111-128] by means of a representation based on the Pochhammer's contour of integration for fractional derivatives in order to derive new expansion formulas for several families of the Hurwitz-Lerch zeta function. Special cases are also given.
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Dates et versions

hal-04466012 , version 1 (19-02-2024)

Identifiants

  • HAL Id : hal-04466012 , version 1

Citer

Abdelmejid Bayad, Sébastien Gaboury. FURTHER EXPANSION FORMULAS FOR A CLASS OF GENERALIZED HURWITZ-LERCH ZETA FUNCTIONS OBTAINED BY MEANS OF A NEW LEIBNIZ RULE FOR FRACTIONAL DERIVATIVES. 2024. ⟨hal-04466012⟩
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