English

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}
}
R2 v1 2026-06-23T12:49:45.808Z