Certain integrals of generalized hypergeometric and confluent hypergeometric functions (original) (raw)

Certain Integrals Associated with Generalized Hypergeometric Functions

Acta Universitatis Apulensis

The present paper deals with the three new integral formulas involving the extended generalized hypergeometric function and are expressed in term of the generalized hypergeometric functions. Some important particular cases involving the extended Gauss hypergeometric and confluent hypergeometric functions are also pointed out.

New Generalized Hypergeometric Functions

Ikonion Journal of Mathematics

The classical Gauss hypergeometric function and the Kumar confluent hypergeometric function are defined using a classical Pochammer symbol , and a factorial function. This research paper will present a two-parameter Pochhammer symbol, and discuss some of its properties such as recursive formulae and integral representation. In addition, the generalized Gauss and Kumar confluent hypergeometric functions are defined using a two-parameter Pochhammer symbol and two-parameter factorial function and some of the properties of the new generalized hypergeometric functions were also discussed.

A Study of Extended Beta, Gauss and Confluent Hypergeometric Functions

International Journal of Apllied Mathematics, 2020

In the present research note, we define a new extension of beta function by making use of the multi-index Mittag-Leffler function. Here, first we derive its fundamental properties and then we present a new type of beta distribution as an application of our proposed beta function. Moreover, we present a new extension of Gauss and confluent hypergeometric functions in terms of our newly introduced beta function. Some interesting properties of our extended hypergeometric functions (like integral representations, differential formulae, transformations and summation formulae and a generating relation) are also indicated in the last section.

Certain Properties of the Generalized Gauss Hypergeometric Functions

Applied Mathematics & Information Sciences, 2014

In this paper, we aim at establishing certain integral transform and fractional integral formulas for the generalized Gauss hypergeometric functions, which was introduced and studied byÖzergin et al. [J. Comput. Appl. Math. 235(2011), 4601-4610]. All the results derived here are of general character and can yield a number of (known and new) results in the theory of integral transforms and fractional integrals.

Extended Generalized Τ -Gauss’ Hypergeometric Functions and Their Applications

South East Asian J. of Mathematics and Mathematical Sciences

In this article, by means of the extended beta function, we introduce new extension of the generalized τ -Gauss’ hypergeometric functions and present some new integral and series representations (including the one obtained by adopt- ing the well-known Ramanujan’s Master Theorem). We also consider some new and known results as consequences of our proposed extension of the generalized τ -Gauss hypergeometric function.

Further results on generalized hypergeometric functions

Applied Mathematics and Computation, 2003

Recently, Virchenko et al. [Integral Transform. and Spec. Funct. 12 (1) (2001) 89-100] have defined and studied a generalized hypergeometric function of the form 2 R s 1 ða; b; c; s; zÞ ¼ CðcÞ CðbÞCðc À bÞ Z 1 0 t bÀ1 ð1 À tÞ cÀbÀ1 ð1 À zt s Þ dt:

Properties and Applications of Extended Hypergeometric Functions

2014

In this article, we study several properties of extended Gauss hypergeometric and extended confluent hypergeometric functions. We derive several integrals, inequalities and establish relationship between these and other special functions. We also show that these functions occur naturally in statistical distribution theory. MSC:33C90

New extension of beta, Gauss and confluent hypergeometric functions

Cumhuriyet Science Journal, 2021

There are many extensions and generalizations of Gamma and Beta functions in the literature. However, a new extension of the extended Beta function , 1 2 ; 1 , 2 (1 , 2) was introduced and presented here because of its important properties. The new extended Beta function has symmetric property, integral representations, Mellin transform, inverse Mellin transform and statistical properties like Beta distribution, mean, variance, moment and cumulative distribution which ware also presented. Finally, the new extended Gauss and Confluent Hypergeometric functions with their propertied were introduced and presented.