ON A NEW GENERALIZED BETA FUNCTION DEFINED BY THE GENERALIZED WRIGHT FUNCTION AND ITS APPLICATIONS

Abstract

Various extensions of classical gamma, beta, Gauss hypergeometric and confluent hypergeometric functions have been proposed recently by many researchers. In this paper, further generalized extended beta function with some of its properties like summation formulas, Integral representations, connections with other special functions such as incomplete gamma, classical beta, classical Wright, hypergeometric, error, Fox-H, Fox-Wright, Meijer-G functions are obtained. Beta distribution together with-it corresponding moment, mean, variance, moment generating function and cumulative distribution are also presented. Moreover, the generalized beta function is used to generalized classical and other related extended Gauss, Kumar confluent, Appell’s and Lauricella’s hypergeometric functions with their integral representations, differential, difference, summation and transformations formulas.

Keywords

• appell-lauricella function
• beta distribution
• confluent hypergeometric function
• gauss hypergeometric function
• wright function