Solution of a Class of the Riemann-Papperitz Equation with Two Singular Points

TL;DR

This paper solves a specific class of Riemann-Papperitz equations with two singular points by transforming them into a hypergeometric form using a conformal map, providing explicit solutions in terms of hypergeometric functions.

Contribution

It introduces a method to explicitly solve Riemann-Papperitz equations with two singular points via conformal mapping and hypergeometric functions, expanding the solution techniques for such equations.

Findings

Explicit solutions in terms of hypergeometric functions

Mapping singular points to standard positions

Applicable to equations with two singular points

Abstract

This paper provides the solution of the Riemann-Papperitz equation with singular points at z=-i,i.This solution is obtained by mapping the singular points into points 0,infinity. The solution is then obtained in terms of the Gauss hypergeometric function.