Series Solution to a Fuchsian‐Type Differential Equation in Terms of Orthogonal Polynomials

In this paper, we study a thirteen‐parameter Fuchsian‐type second‐order linear differential equation that involves five regular singularities. By employing a tridiagonal representation technique, we formulate four cases under which the series solutions of the equation are obtained in terms of Jacobi polynomials. The coefficients in the series solution found under these conditions are the normalized Wilson polynomials, a scaled version of the normalized Wilson polynomials, and a new modified Wilson polynomial. We study the spectral properties of this newly encountered polynomial and provide a method that approximates the unknown measure of orthogonality corresponding to these new modified Wilson polynomials.