Heun equations and combinatorial identities

Abstract

Heun functions are important for many applications in mathematics, physics and in thus in interdisciplinary phenomena modelling. They satisfy second order differential equations and are usually represented by powerseries. Closed forms and simpler polynomial representations are useful. Therefore, we study and derive closed formsfor several families of Heun functions related to classical entropies. By comparing two expressions of the same Heunfunction, we get several combinatorial identities generalizing some classical ones.