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 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.