Version 1
: Received: 5 January 2018 / Approved: 9 January 2018 / Online: 9 January 2018 (07:08:48 CET)
How to cite:
Rahman, G.; Kanwal, G.; Nisar, K.S.; Ghaffar, A. A New Extension of Beta and Hypergeometric Functions. Preprints2018, 2018010074. https://doi.org/10.20944/preprints201801.0074.v1
Rahman, G.; Kanwal, G.; Nisar, K.S.; Ghaffar, A. A New Extension of Beta and Hypergeometric Functions. Preprints 2018, 2018010074. https://doi.org/10.20944/preprints201801.0074.v1
Rahman, G.; Kanwal, G.; Nisar, K.S.; Ghaffar, A. A New Extension of Beta and Hypergeometric Functions. Preprints2018, 2018010074. https://doi.org/10.20944/preprints201801.0074.v1
APA Style
Rahman, G., Kanwal, G., Nisar, K.S., & Ghaffar, A. (2018). A New Extension of Beta and Hypergeometric Functions. Preprints. https://doi.org/10.20944/preprints201801.0074.v1
Chicago/Turabian Style
Rahman, G., Kottakkaran Sooppy Nisar and Abdul Ghaffar. 2018 "A New Extension of Beta and Hypergeometric Functions" Preprints. https://doi.org/10.20944/preprints201801.0074.v1
Abstract
The main objective of this paper is to introduce a further extension of extended (p, q)-beta function by considering two Mittag-Leffler function in the kernel. We investigate various properties of this newly defined beta function such as integral representations, summation formulas and Mellin transform. We define extended beta distribution and its mean, variance and moment generating function with the help of extension of beta function. Also, we establish an extension of extended (p, q)-hypergeometric and (p, q)-confluent hypergeometric functions by using the extension of beta function. Various properties of newly defined extended hypergeometric and confluent hypergeometric functions such as integral representations, Mellin transformations, differentiation formulas, transformation and summation formulas are investigated.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
