An extension of beta function, its statistical distribution, and associated fractional operator

Recently, various forms of extended beta function have been proposed and presented by many researchers. The principal goal of this paper is to present another expansion of beta function using Appell series and Lauricella function and examine various properties like integral representation and summat...

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Published in:	Advances in difference equations Vol. 2020; no. 1; pp. 1 - 17
Main Authors:	Chandola, Ankita, Mishra Pandey, Rupakshi, Agarwal, Ritu, Dutt Purohit, Sunil
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 04.12.2020 Springer Nature B.V SpringerOpen
Subjects:	Analysis Appell series Applications Difference and Functional Equations Distribution functions Extended beta function Extended confluent hypergeometric function Extended hypergeometric function Functional Analysis Hypergeometric functions Integrals Lauricella function Mathematics Mathematics and Statistics Methods Operators (mathematics) Ordinary Differential Equations Partial Differential Equations Probability distribution Representations Statistical distribution Topics in Special Functions and q-Special Functions: Theory Extended beta function Extended confluent hypergeometric function Statistical distribution Riemann–Liouville fractional operator Extended hypergeometric function Lauricella function Appell series
ISSN:	1687-1847, 1687-1839, 1687-1847
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Abstract	Recently, various forms of extended beta function have been proposed and presented by many researchers. The principal goal of this paper is to present another expansion of beta function using Appell series and Lauricella function and examine various properties like integral representation and summation formula. Statistical distribution for the above extension of beta function has been defined, and the mean, variance, moment generating function and cumulative distribution function have been obtained. Using the newly defined extension of beta function, we build up the extension of hypergeometric and confluent hypergeometric functions and discuss their integral representations and differentiation formulas. Further, we define a new extension of Riemann–Liouville fractional operator using Appell series and Lauricella function and derive its various properties using the new extension of beta function.
AbstractList	Recently, various forms of extended beta function have been proposed and presented by many researchers. The principal goal of this paper is to present another expansion of beta function using Appell series and Lauricella function and examine various properties like integral representation and summation formula. Statistical distribution for the above extension of beta function has been defined, and the mean, variance, moment generating function and cumulative distribution function have been obtained. Using the newly defined extension of beta function, we build up the extension of hypergeometric and confluent hypergeometric functions and discuss their integral representations and differentiation formulas. Further, we define a new extension of Riemann–Liouville fractional operator using Appell series and Lauricella function and derive its various properties using the new extension of beta function. Abstract Recently, various forms of extended beta function have been proposed and presented by many researchers. The principal goal of this paper is to present another expansion of beta function using Appell series and Lauricella function and examine various properties like integral representation and summation formula. Statistical distribution for the above extension of beta function has been defined, and the mean, variance, moment generating function and cumulative distribution function have been obtained. Using the newly defined extension of beta function, we build up the extension of hypergeometric and confluent hypergeometric functions and discuss their integral representations and differentiation formulas. Further, we define a new extension of Riemann–Liouville fractional operator using Appell series and Lauricella function and derive its various properties using the new extension of beta function.
ArticleNumber	684
Author	Mishra Pandey, Rupakshi Dutt Purohit, Sunil Chandola, Ankita Agarwal, Ritu
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SubjectTerms	Analysis Appell series Applications Difference and Functional Equations Distribution functions Extended beta function Extended confluent hypergeometric function Extended hypergeometric function Functional Analysis Hypergeometric functions Integrals Lauricella function Mathematics Mathematics and Statistics Methods Operators (mathematics) Ordinary Differential Equations Partial Differential Equations Probability distribution Representations Statistical distribution Topics in Special Functions and q-Special Functions: Theory
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Title	An extension of beta function, its statistical distribution, and associated fractional operator
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