Integro-differential Equations and Generalized Hypergeometric Functions

University of Cambridge Integro-diierential Equations and Generalized Hypergeometric Functions Integro-diierential Equations and Generalized Hypergeometric Functions Are Neither Zero nor a Negative In- Teger, and 2 0; 2) There Exist Smooth Functions and Such That the Generalized Hypergeometric Function

This paper is concerned with the integro-diierential equations y 0 (t) = ay(t) + Z 1 0 y(qt) d(q) + Z 1 0 y 0 (qt) d(q); t 0 and y(t) + Z 1 0 y(qt) d(q) + Z 1 0 y 0 (qt) d(q) = 0; t 0; where a is a complex constant, while and are complex-valued functions of bounded variation on 0; 1]. The main motivation for the study of these two equations is that for every integers B + 1 A 0 and real constant...

Notes on differential equations and hypergeometric functions

HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: Horn hypergeometric functions of two variables

The HYPERDIRE is a project devoted to creation of a set of Mathematica based programs for differential reduction of hypergeometric functions. The current version allow to manipulate with full set of Horn hypergeometric functions of two variables (34 functions). PROGRAM SUMMARY Title of program: HYPERDIRE Version: 1.0.0 Release: 1.0.0 Catalogue number : Program obtained from: https://sites.googl...

Generalized basic hypergeometric equations

This paper deals with regular singular generalized q-hypergeometric equations with either “large” or “small” Galois groups. In particular, we consider the fundamental problem of finding appropriate Galoisian substitutes for the usual notion of local monodromy.

Nonlinear Integro - Differential Equations