A new Generalization of Extended Beta and Hypergeometric Functions

A new generalization of extended beta functions by using generalized Mittag-Leffler functions is proposed. Important properties of the generalized beta function and the integral representations are investigated. The generalization of the hypergeometric and Confluent hypergeometric functions is also introduced. Some more properties of these functions such as integral representations, differentiation formulas, transformation and summation formulas, Mellin transformations are also established.

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A new generalized beta function associated with statistical distribution and fractional kinetic equation

Panwar,

Rai,

Pandey

2024

B Soc Paran Mat

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Several authors have extensively investigated beta function, hypergeometric function and confluent hypergeometric function, their extensions and generalizations due to their several application in many areas of engineering, probability theory and science. The main purpose of this paper is to present a new generalization of extended beta function, hypergeometric function and confluent hypergeometric function with the help of m-parameter Mittag-Leffler function, as well as examine some important properties like integral representations, differential formula and summation formulas. We also examine generalized Caputo fractional derivative operator with the help of m-parameter Mittag-Leffler function with associated properties using the generalized beta function. We define a new beta distribution involving the new generalized beta function. The mean, variance, coefficient of variance, moment generating function and characteristic function and cumulative distribution are derived. Further, we derive the solution of fractional Kinetic equation involving generalized hypergeometric function.

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A new Generalization of Extended Beta and Hypergeometric Functions

Cited by 3 publications

References 11 publications

A (p,v)-Extension of Hurwitz-Lerch Zeta Function and its Properties

A (p,v)-Extension of Hurwitz-Lerch Zeta Function and its Properties

Generalization of Beta functions in terms of Mittag-Leffler function

A new generalized beta function associated with statistical distribution and fractional kinetic equation

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