### 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 |

### Fingerprint

### 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

### Cite this

*Applied Mathematics and Computation*,

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

**Generalized confluent hypergeometric solutions of the Heun confluent equation.** / Ishkhanyan, T. A.; Ishkhanyan, A. M.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - Generalized confluent hypergeometric solutions of the Heun confluent equation

AU - Ishkhanyan, T. A.

AU - Ishkhanyan, A. M.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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.

AB - 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.

KW - 02.30.Gp Special functions

KW - 02.30.Hq Ordinary differential equations

KW - 02.30.Mv Approximations and expansions

KW - Bessel function

KW - Confluent Heun equation

KW - Confluent hypergeometric function

KW - Recurrence relation

UR - http://www.scopus.com/inward/record.url?scp=85049789635&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049789635&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2018.06.053

DO - 10.1016/j.amc.2018.06.053

M3 - Article

AN - SCOPUS:85049789635

VL - 338

SP - 624

EP - 630

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -