A New Extension of the τ-Gauss Hypergeometric Function and Its Associated Properties

被引：11

作者：

Srivastava, Hari Mohan ^{[1
,2
,3
]}

Tassaddiq, Asifa ^{[4
]}

Rahman, Gauhar ^{[5
]}

Nisar, Kottakkaran Sooppy ^{[6
]}

Khan, Ilyas ^{[7
]}

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada

[2] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan

[3] Azerbaijan Univ, Dept Math & Informat, 71 Jeyhun Hajibeyli St, AZ-1007 Baku, Azerbaijan

[4] Majmaah Univ, Coll Comp & Informat Sci, Al Majmaah 11952, Saudi Arabia

[5] Shaheed Benazir Bhutto Univ, Dept Math, Sheringal 18000, Upper Dir, Pakistan

[6] Prince Sattam Bin Abdulaziz Univ, Coll Arts & Sci, Dept Math, Wadi Aldawaser 11991, Saudi Arabia

[7] Majmaah Univ, Coll Sci Al Zulfi, Dept Math, Al Majmaah 11952, Saudi Arabia

来源：

MATHEMATICS | 2019年 / 7卷 / 10期

关键词：

gamma function and its extension; Pochhammer symbol and its extensions; hypergeometric function and its extensions; tau-Gauss hypergeometric function and its extensions; tau-Kummer hypergeometric function; Fox-Wright function; POCHHAMMER SYMBOL; GAMMA;

D O I：

10.3390/math7100996

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we define an extended version of the Pochhammer symbol and then introduce the corresponding extension of the tau-Gauss hypergeometric function. The basic properties of the extended tau-Gauss hypergeometric function, including integral and derivative formulas involving the Mellin transform and the operators of fractional calculus, are derived. We also consider some new and known results as consequences of our proposed extension of the tau-Gauss hypergeometric function.

引用

页数：9

共 29 条

[1] Extension of Pochhammer symbol, generalized hypergeometric function and τ-Gauss hypergeometric function
Yadav, Komal Singh
Sharan, Bhagwat
Verma, Ashish
ANALYSIS-INTERNATIONAL MATHEMATICAL JOURNAL OF ANALYSIS AND ITS APPLICATIONS, 2024, : 61 - 72
[2] A new extension of Srivastava's triple hypergeometric functions and their associated properties
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Rahman, Gauhar
Anjum, Zunaira
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ANALYSIS-INTERNATIONAL MATHEMATICAL JOURNAL OF ANALYSIS AND ITS APPLICATIONS, 2021, 41 (01): : 13 - 24
[3] A (p, q)-extension of Srivastava's triple hypergeometric function HB and its properties
Dar, S. A.
Paris, R. B.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2019, 348 : 237 - 245
[4] An Extension of the Mittag-Leffler Function and Its Associated Properties
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Anjum, Zunaira
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Abdeljawad, Thabet
ADVANCES IN MATHEMATICAL PHYSICS, 2020, 2020
[5] A New Extension of the Pochhammer Symbol and Its Application to Hypergeometric Functions
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Rahman G.
Ullah Z.
Ghaffar A.
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International Journal of Applied and Computational Mathematics, 2019, 5 (6)
[6] Properties and Applications of a New Extended Gamma Function Involving Confluent Hypergeometric Function
Saboor, Abdus
Rahman, Gauhar
Ali, Hazrat
Nisar, Kottakkaran Sooppy
Abdeljawad, Thabet
JOURNAL OF MATHEMATICS, 2021, 2021
[7] AN EXTENSION OF THE BETA FUNCTION EXPRESSED AS A COMBINATION OF CONFLUENT HYPERGEOMETRIC FUNCTIONS
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HONAM MATHEMATICAL JOURNAL, 2021, 43 (02): : 183 - 197
[8] An Extension of Pochhammer's Symbol and its Application to Hypergeometric Functions
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Milovanovic, Gradimir V.
FILOMAT, 2017, 31 (02) : 207 - 215
[9] A New Generalization of Confluent Hypergeometric Function and Whittaker Function
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Usman, T.
Ghayasuddin, M.
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2020, 38 (02): : 9 - 26
[10] Investigation for the k-analogue of τ-Gauss hypergeometric matrix functions and associated fractional calculus
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Hidan, Muajebah
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LINEAR & MULTILINEAR ALGEBRA, 2024, 72 (05) : 737 - 750

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