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Vol.5 , No. 1, Publication Date: Jan. 18, 2018, Page: 24-34
 have been studied in recent literature. The main object of this paper is to express explicitly the generalization of the classical generalized hypergeometric function <i>pFq</i> in terms of the classical generalized hypergeometric function itself; moreover, the Pfaff-Saalschütz theorem is given as special case from it, and some new integrals using the generalized Gauss hypergeometric functions are obtained and many important results are noted.&picture=http://www.aascit.org/aascit/decorators/img/journal/921.jpg)
| [1] | Salma Ibrahim El-Soubhy, Department of Mathematics, Faculty of Science, Taibah University, Al-Medinah Al-munawwarh, Saudi Arabia. |
| [2] | Mareiah Mansoor Al-Khalaf, Department of Mathematics, Faculty of Science, Taibah University, Al-Medinah Al-munawwarh, Saudi Arabia. |
| [3] | Aziza Salamah Al-Rasheedi, Department of Mathematics, Faculty of Science, Taibah University, Al-Medinah Al-munawwarh, Saudi Arabia. |
| [4] | Ghofran Abdul-Rahman Al-Hendi, Department of Mathematics, Faculty of Science, Taibah University, Al-Medinah Al-munawwarh, Saudi Arabia. |
| [5] | Sayfiah Karazim Al-Juhani, Department of Mathematics, Faculty of Science, Taibah University, Al-Medinah Al-munawwarh, Saudi Arabia. |
| [6] | Sumayyah Ahmed Al-Ahmadi, Department of Mathematics, Faculty of Science, Taibah University, Al-Medinah Al-munawwarh, Saudi Arabia. |
Recently, some generalizations of the generalized famous special functions (e.g. Gamma function, Beta function, Gauss hypergeometric function,…etc) have been studied in recent literature. The main object of this paper is to express explicitly the generalization of the classical generalized hypergeometric function pFq in terms of the classical generalized hypergeometric function itself; moreover, the Pfaff-Saalschütz theorem is given as special case from it, and some new integrals using the generalized Gauss hypergeometric functions are obtained and many important results are noted.
Keywords
Gamma Function, Beta Function, Hypergeometric Function, Confluent Hypergeometric Function, Pfaff-Saalschütz Theorem, Generalized Hypergeometric Functions
Reference
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| [10] | S. I. EL-Soubhy, On the generalization of hypergeometric and confluent hypergeometric functions and their applications for finding the derivatives of the generalized Jacobi Polynomials, Intertional Journal of Mathematical Analysis and applications, vol. 2, No. 6, (2016) 79-90. |
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