A novel Kind of the multi-index Beta, Gauss, and confluent hypergeometric functions
Volume 23, Issue 2, pp 145--154
http://dx.doi.org/10.22436/jmcs.023.02.07
Publication Date: October 22, 2020
Submission Date: August 01, 2020
Revision Date: September 08, 2020
Accteptance Date: September 18, 2020
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Authors
Musharraf Ali
- Department of Mathematics , G.F. College, Shahjahanpur-242001, India.
Mohd Ghayasuddin
- Department of Mathematics, Integral University Campus, Shahjahanpur-242001, India.
Waseem A. Khan
- Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box: 1664, Al Khobar 31952, Saudi Arabia.
Kottakkaran Sooppy Nisar
- Department of Mathematics, College of Arts and Sciences, Wadi Aldawser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia.
Abstract
This research article elaborates on a novel expansion of the beta function by using the multi-index Mittag-Leffler function. Here, we derive some basic properties of this new beta function and then present a new type of beta dispersal as an application of our proposed beta function. We also introduce a novel expansion of Gauss and confluent hypergeometric functions for our newly initiated beta function. Some important properties of our proposed hypergeometric functions (like integral representations, differential formulae, transformations formulae, summation formulae, and a generating relation) are also pointed out systematically.
Share and Cite
ISRP Style
Musharraf Ali, Mohd Ghayasuddin, Waseem A. Khan, Kottakkaran Sooppy Nisar, A novel Kind of the multi-index Beta, Gauss, and confluent hypergeometric functions, Journal of Mathematics and Computer Science, 23 (2021), no. 2, 145--154
AMA Style
Ali Musharraf, Ghayasuddin Mohd, Khan Waseem A., Nisar Kottakkaran Sooppy, A novel Kind of the multi-index Beta, Gauss, and confluent hypergeometric functions. J Math Comput SCI-JM. (2021); 23(2):145--154
Chicago/Turabian Style
Ali, Musharraf, Ghayasuddin, Mohd, Khan, Waseem A., Nisar, Kottakkaran Sooppy. "A novel Kind of the multi-index Beta, Gauss, and confluent hypergeometric functions." Journal of Mathematics and Computer Science, 23, no. 2 (2021): 145--154
Keywords
- Beta function
- extended beta function
- Gauss hypergeometric function
- confluent hypergeometric function
- multi-index Mittag-Leffler function
MSC
- 33B15
- 33B20
- 33C05
- 33C15
- 33E12
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