A New Extension of the Pochhammer Symbol and Its Application to Hypergeometric Functions

Our main goal in this present paper is to define first a new extension of the Pochhammer symbol and the gamma functions which involving the Mittag-Leffler function in their kernels. By using this extended Pochhammer symbol, we then introduce and investigate the corresponding extension of the general...

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Bibliographic Details
Published in:International journal of applied and computational mathematics Vol. 5; no. 6; pp. 1 - 13
Main Authors: Safdar, Maryam, Rahman, Gauhar, Ullah, Zafar, Ghaffar, Abdul, Nisar, Kottakkaran Sooppy
Format: Journal Article
Language:English
Published: New Delhi Springer India 01.12.2019
Springer Nature B.V
Subjects:
Applications of Mathematics
Applied mathematics
Computational mathematics
Computational Science and Engineering
Derivatives
Fractional calculus
Gamma function
Hypergeometric functions
Integrals
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Mellin transforms
Nuclear Energy
Operations Research/Decision Theory
Original Paper
Theoretical
Pochhammer symbol
33B15
Gauss hypergeometric function
33C45
33C65
33C20
Gamma function
33C90
Generalized hypergeometric function
33C05
ISSN:2349-5103, 2199-5796
Online Access:Get full text
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Summary:Our main goal in this present paper is to define first a new extension of the Pochhammer symbol and the gamma functions which involving the Mittag-Leffler function in their kernels. By using this extended Pochhammer symbol, we then introduce and investigate the corresponding extension of the generalized hypergeometric functions and of some of its special cases. Also, we establish the basic properties and results for the extended τ -Gauss hypergeometric function, which includes integral and derivative formulas involving the Mellin transform and fractional calculus approaches. Some new and known results as consequences of our proposed extension of the τ -Gauss hypergeometric function are also established.
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ISSN:2349-5103
2199-5796
DOI:10.1007/s40819-019-0733-9