DEGENERATE GAUSS 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...

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.

Gauss Quadrature Approximations to Hypergeometric and Confluent Hypergeometric Functions

Transformations of some Gauss hypergeometric functions

This paper presents explicit algebraic transformations of some Gauss hypergeometric functions. Specifically, the transformations considered apply to hypergeometric solutions of hypergeometric differential equations with the local exponent differences 1/k, 1/l, 1/m such that k, l,m are positive integers and 1/k + 1/l+ 1/m < 1. All algebraic transformations of these Gauss hypergeometric functions...

Algebraic transformations of Gauss hypergeometric functions

This 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.