New extension of beta, Gauss and confluent hypergeometric functions

Gauss Quadrature Approximations to Hypergeometric and Confluent Hypergeometric Functions

Degenerate Gauss hypergeometric functions

Throughout the paper, we denote this equation by E(a, b, c). Since Kummer we know that in general there are 24 hypergeometric series which express solutions of E(a, b, c). The subject of this paper is Gauss hypergeometric functions when some or all of the numbers a, b, c, c − a, c − b, a − b, c − a − b are integers. We refer to these functions and to corresponding hypergeometric equations as de...

New Laplace transforms of Kummer's confluent hypergeometric functions

In this paper we aim to show how one can obtain so far unknown Laplace transforms of three rather general cases of Kummer’s confluent hypergeometric function 1F1(a; b; x) by employing generalizations of Gauss’s second summation theorem, Bailey’s summation theorem and Kummer’s summation theorem obtained earlier by Lavoie, Grondin and Rathie. The results established may be useful in theoretical p...

Transformations of Gauss hypergeometric functions

The paper classifies algebraic transformations of Gauss hypergeometric functions and pull-back transformations between hypergeometric differential equations. This classification recovers the classical transformations of degree 2, 3, 4, 6, and finds other transformations of some special classes of the Gauss hypergeometric function.

On an Extension of Extended Beta and Hypergeometric Functions

Abstract. Motivated mainly by certain interesting recent extensions of the Gamma, Beta and hypergeometric functions, we introduce here new extensions of the Beta function, hypergeometric and confluent hypergeometric functions. We systematically investigate several properties of each of these extended functions, such as their various integral representations, Mellin transforms, derivatives, tran...