The Jacobi-type polynomials and general Heun equations

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.(c) 2023 Elsevier Ltd. All rights reserved.

Automated summary

In this paper, the asymptotic solutions of the general Heun equation are presented using orthogonal polynomials with perturbed classical Jacobi weights. A double limit approach is applied, which includes changes in variables or scaling. The second-order differential equations satisfied by the orthogonal polynomials generated by the given Jacobi-type weights are constructed as an approximation for the general Heun equation. (c) 2023 Elsevier Ltd. All rights reserved.