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

Advances in Difference Equations

article

Chandola, Ankita¹  Mishra Pandey, Rupakshi¹  Agarwal, Ritu²  Dutt Purohit, Sunil³ 

[1] Amity Institute of Applied Sciences, Amity University;Malaviya National Institute of Technology;Rajasthan Technical University

关键词: Extended beta function;    Appell series;    Lauricella function;    Extended hypergeometric function;    Extended confluent hypergeometric function;    Statistical distribution;    Riemann–Liouville fractional operator;   

DOI  :  10.1186/s13662-020-03142-6

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY