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In this paper, we establish two general transformation formulas for Exton’s quadruple hypergeometric functions K5 and K12 by application of the generalized Kummer’s summation theorem. Further, a number of generating functions for Jacobi polynomials are also derived as an applications of our main results.

The aim of this paper is to derive some of Generating Functions for the quadruple Hypergeometric functions ( 3 10 13 16 18 K ,K ,K ,K and K ). The results are derived with the help of Laplace integral. A number of Generating Functions of such other types of hypergeometric functions are also derived as special cases of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we establish a general summation formula for the confluent hypergeometric function Φ(2r) 2 of several variables by applying the generalized Kummer's summation theorem due to Lavoie et al. As an applications of our main result, we obtain certain new summation formulas for the confluent hypergeometric function Φ(4) 2. Also some summation and transformation formulas including a results obtained recently by Choi and Rathie have been obtained as special cases. [ABSTRACT FROM AUTHOR]

In this paper, we have established two general integral formulas involving Humbert hypergeometric functions of two variablesΦ2 and Ψ2 . The results are obtained with the help of a generalization of classical Kummer's summation theorem on the sum of the series 2F1(-1) due to Lavoie et al. [5]. Some interesting applications are also presented. [ABSTRACT FROM AUTHOR]

The aim of this research paper is to obtain two extension formulas for the first and second kind of Lauricella's functions of three variables with the help of generalized Dixon's summation theorem, which was obtained by Lavoie et al. In addition to this, two extension formulas for the second and third kind of Appell's functions are obtained as a consequence of the above mentioned results . Furthermore, some transformation formulas involving Exton's double hypergeometric series are obtained as an applications of our main results. [ABSTRACT FROM AUTHOR]

The main object of the present work is to derive some general integral formulas (single, double and multiple) involving Laguerre polynomials of several variables. A number of known and new integral formulas involving Laguerre polynomials of two and three variables are obtained as special cases of our general formulas. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish an extension formulas for the first kind of Lauricella's functions of three variables. The results are obtained with the help of two interesting special cases of the generalizations of Watson's summation theorem given by Lavoie et al.[5]. Some interesting special cases are also presented. [ABSTRACT FROM AUTHOR]