Explicit formulas for parametrized families of irreducible algebraic Appell, Lauricella and Horn functions

TL;DR

This paper provides explicit formulas for families of algebraic Appell, Lauricella, and Horn functions depending on a parameter, advancing understanding of their algebraic and differential properties.

Contribution

It introduces explicit formulas for algebraic families of these functions, extending previous work on specific cases and providing solutions to their differential systems.

Findings

Explicit formulas for algebraic families of functions

Solutions of differential systems in closed form

Extension of previous algebraic function classifications

Abstract

For suitable choices of the parameters the Appell, Lauricella and Horn functions are algebraic. In a previous paper we showed that there exist families of algebraic functions for the F_4, F_C, G_3, H_4, H_5 and H_7 functions, depending on one parameter r. For each of these we give a solution of the form f^r.g of the system of differential equations and give formulas for f and g.