Eulerian integral associated with product of two multivariable A-functions, generalized Lauricella function and a class of polynomial and the multivariable I-function defined by Nambisan I

2016 ◽  
Vol 40 (1) ◽  
pp. 79-91
Author(s):  
F.Y Ayant
Keyword(s):  
Lauricella Function

Analytic continuations of the Lauricella function

1978 ◽  
Vol 19 (12) ◽  
pp. 2485-2490 ◽  
Author(s):  
A. R. Sud ◽  
K. K. Sud
Keyword(s):  
Lauricella Function

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

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ankita Chandola ◽  
Rupakshi Mishra Pandey ◽  
Ritu Agarwal ◽  
Sunil Dutt Purohit
Keyword(s):  
Beta Function ◽  
Summation Formula ◽  
Moment Generating Function ◽  
Statistical Distribution ◽  
Integral Representations ◽  
Cumulative Distribution ◽  
Fractional Operator ◽  
Confluent Hypergeometric Functions ◽  
Lauricella Function ◽  
Extended Beta Function

AbstractRecently, 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.

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