The Jacobi-type polynomials and general Heun equations

Abstract

In this paper, we present the asymptotic “solutions” of the general Heun equation in terms of the orthogonal polynomials with respect to certain perturbed “classical” Jacobi weights. Our approach employs a double limit, which includes changes in variables or scaling. We construct the second-order differential equations satisfied by the orthogonal polynomials generated by the given Jacobi-type weights as an approximation for the general Heun equation.