Certain Class of Generating Functions for the Incomplete Hypergeometric Functions

Generating functions for the generalized Gauss hypergeometric functions

Formulas and identities involving many well-known special functions (such as the Gamma and Beta functions, the Gauss hypergeometric function, and so on) play important rôles in themselves and in their diverse applications. Various families of generating functions have been established by a number of authors in many different ways. In this paper, we aim at establishing some (presumably new) gene...

The Uniformization of Certain Algebraic Hypergeometric Functions

The hypergeometric functions nFn−1 are higher transcendental functions, but for certain parameter values they become algebraic. This occurs, e.g., if the defining hypergeometric differential equation has irreducible but imprimitive monodromy. It is shown that many algebraic nFn−1’s of this type can be represented as combinations of certain explicitly algebraic functions of a single variable, i....

Certain Incomplete Numerical Functions*

Generating Kummer Type Formulas for Hypergeometric Functions

Kummer type formulas are identities of hypergeometric series. A symmetry by the permutations of n-letters yields these formulas. We will present an algorithmic method to derive known and new Kummer type formulas. The algorithm utilizes several algorithms in algebra and geometry for generating Kummer type formulas.

Integral Properties of Zonal Spherical Functions, Hypergeometric Functions and Invariant

Some integral properties of zonal spherical functions, hypergeometric functions and invariant polynomials are studied for real normed division algebras.