A note on the generalized-hypergeometric solutions of general and single-confluent Heun equations
Classical Analysis and ODEs
2021-03-04 v1
Abstract
We review the series solutions of the general and single-confluent Heun equations in terms of powers, ordinary-hypergeometric and confluent-hypergeometric functions. The conditions under which the expansions reduce to finite sums as well as the cases when the coefficients of power-series expansions obey two-term recurrence relations are discussed. Infinitely many cases for which a solution of a general or single-confluent Heun equation is written through a single generalized hypergeometric function are indicated. It is shown that the parameters of this generalized hypergeometric function are the roots of a certain polynomial equation, which we explicitly present for any given order.
Cite
@article{arxiv.2103.02053,
title = {A note on the generalized-hypergeometric solutions of general and single-confluent Heun equations},
author = {D. Yu. Melikdzhanian and A. M. Ishkhanyan},
journal= {arXiv preprint arXiv:2103.02053},
year = {2021}
}