Heun equations and combinatorial identities

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 power series. Closed forms and simpler polynomial representations are useful. Therefore, we study and derive closed forms for several families of Heun functions related to classical entropies. By comparing two expressions of the same Heun function, we get several combinatorial identities generalizing some classical ones.