[Fonctions τ-hypergéométriques étendues et leurs propriétés]
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 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 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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@article{CRMATH_2015__353_5_421_0,
author = {Parmar, Rakesh K.},
title = {Extended \protect\emph{\ensuremath{\tau}}-hypergeometric functions and associated properties},
journal = {Comptes Rendus. Math\'ematique},
pages = {421--426},
publisher = {Elsevier},
volume = {353},
number = {5},
year = {2015},
doi = {10.1016/j.crma.2015.01.016},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2015.01.016/}
}
TY - JOUR AU - Parmar, Rakesh K. TI - Extended τ-hypergeometric functions and associated properties JO - Comptes Rendus. Mathématique PY - 2015 SP - 421 EP - 426 VL - 353 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2015.01.016/ DO - 10.1016/j.crma.2015.01.016 LA - en ID - CRMATH_2015__353_5_421_0 ER -
%0 Journal Article %A Parmar, Rakesh K. %T Extended τ-hypergeometric functions and associated properties %J Comptes Rendus. Mathématique %D 2015 %P 421-426 %V 353 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2015.01.016/ %R 10.1016/j.crma.2015.01.016 %G en %F CRMATH_2015__353_5_421_0
Parmar, Rakesh K. Extended τ-hypergeometric functions and associated properties. Comptes Rendus. Mathématique, Tome 353 (2015) no. 5, pp. 421-426. doi : 10.1016/j.crma.2015.01.016. http://archive.numdam.org/articles/10.1016/j.crma.2015.01.016/
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