Comptes Rendus
no. 5
Mathematical analysis/Complex analysis
Extended τ-hypergeometric functions and associated properties
[Fonctions τ-hypergéométriques étendues et leurs propriétés]

Présenté par : the Editorial Board

Rakesh K. Parmar1
1 Department of Mathematics, Government College of Engineering and Technology, Bikaner 334004, Rajasthan State, India
Comptes Rendus. Mathématique, Volume 353 (2015) no. 5, pp. 421-426.

Récemment, une extension du symbole de Pochhammer a été utilisée pour introduire et étudier une famille de fonctions hypergéométriques généralisées [Srivastava et al. (2014) [11]]. L'objet de cette Note est de présenter une extension des fonctions τ-hypergéométriques de Gauss R1τ2(z) et d'étudier plusieurs de leurs propriétés, incluant, par exemple, leurs représentations intégrales, les formules de dérivées, les transformées de Mellin et les opérateurs de calcul fractionnaire. Quelques cas particuliers intéressants de nos résultats principaux sont également signalés.

Recently, an extension of the Pochhammer symbol was used in order to introduce and investigate a family of generalized hypergeometric functions [Srivastava et al. (2014) [11]]. The main object of this paper is to present an extension of the τ-Gauss hypergeometric functions R1τ2(z) and investigate its several properties, including, for example, its integral representations, derivative formulas, Mellin transforms and fractional calculus operators. Some interesting special cases of our main results are also pointed out.

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Accepté le :
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DOI : 10.1016/j.crma.2015.01.016
Rakesh K. Parmar 1

1 Department of Mathematics, Government College of Engineering and Technology, Bikaner 334004, Rajasthan State, India 
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Rakesh K. Parmar. Extended τ-hypergeometric functions and associated properties. Comptes Rendus. Mathématique, Volume 353 (2015) no. 5, pp. 421-426. doi : 10.1016/j.crma.2015.01.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.01.016/

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