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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-03142-6