2 HEUN’S EQUATION, GENERALIZED HYPERGEOMETRIC FUNCTION AND EXCEPTIONAL JACOBI POLYNOMIAL

Abstract

We study Heun's differential equation in the case that one of the singularities is apparent. In particular, we propose a conjecture that solutions of Heun's equation in this case also satisfy a generalized hypergeometric equation, which can be described in a more general form, and establish it in some cases. We demonstrate the application of our results to exceptional Jacobi polynomials.