### Abstract

We show that the Heun confluent equation admits infinitely many solutions in terms of the confluent generalized hypergeometric functions. For each of these solutions a characteristic exponent of a regular singularity of the Heun confluent equation is a non-zero integer and the accessory parameter obeys a polynomial equation. Each of the solutions can be written as a linear combination with constant coefficients of a finite number of either the Kummer confluent hypergeometric functions or the Bessel functions.

Original language | English |
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Pages (from-to) | 624-630 |

Number of pages | 7 |

Journal | Applied Mathematics and Computation |

Volume | 338 |

DOIs | |

Publication status | Published - 1 Dec 2018 |

### Keywords

- 02.30.Gp Special functions
- 02.30.Hq Ordinary differential equations
- 02.30.Mv Approximations and expansions
- Bessel function
- Confluent Heun equation
- Confluent hypergeometric function
- Recurrence relation

### ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics

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## Cite this

Ishkhanyan, T. A., & Ishkhanyan, A. M. (2018). Generalized confluent hypergeometric solutions of the Heun confluent equation.

*Applied Mathematics and Computation*,*338*, 624-630. https://doi.org/10.1016/j.amc.2018.06.053