Extended Gamma, Beta and Hypergeometric Functions: Properties and Applications
Extended gamma, beta and hypergeometric functions
Keywords:Gamma function, beta function, hypergeometric functions, pochhammer symbol, beta distribution
The main objective of this paper is to study the newly introduced extended gamma function and present some properties of the existing extended beta and hypergeometric functions with their properties such as integral formulas, functional relations, differential formulas, summation formulas, recurrence relations and the Mellin transform. In addition, applications of the extended beta function to statistical distributions have been discussed by providing mean, variance, coefficient of variance, moment generating function, cumulative distribution and reliability function of the new extended beta distribution.