1993/07/07 by Galliano Valent, Valent, Galliano
Chemistry · Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Molecular spectroscopy and chirality #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.math/9307204
openalex publication_date 1993/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The generating function of Stieltjes-Carlitz polynomials is a solution of\nHeun's differential equation and using this relation Carlitz was the first to\nget exact closed forms for some Heun functions. Similarly the associated\nStieltjes-Carlitz polynomials lead to a new differential equation which we call\nassociated Heun. Thanks to the link with orthogonal polynomials we are able to\ndeduce two integral relations connecting associated Heun functions with\ndifferent parameters and to exhibit the set of associated Heun functions which\ngeneralize Carlitz's. Part of these results were used by the author to derive\nthe Stieltjes transform of the measure of orthogonality for the associated\nStieltjes-Carlitz polynomials using asymptotic analysis; here we present a new\nderivation of this result.\n