Confluent hypergeometric expansions of the confluent Heun function governed by two-term recurrence relations
Classical Analysis and ODEs
2019-12-19 v1
Abstract
We show that there exist infinitely many nontrivial choices of parameters of the single confluent Heun equation for which the three-term recurrence relations governing the expansions of the solutions in terms of the confluent hypergeometric functions 1F1 and 0F1 are reduced to two-term ones. In such cases the expansion coefficients are explicitly calculated in terms of the Euler gamma functions.
Keywords
Cite
@article{arxiv.1912.08623,
title = {Confluent hypergeometric expansions of the confluent Heun function governed by two-term recurrence relations},
author = {T. A. Ishkhanyan and V. P. Krainov and A. M. Ishkhanyan},
journal= {arXiv preprint arXiv:1912.08623},
year = {2019}
}