Solutions of a Confluent Modification of the General Heun Equation in Terms of Generalized Hypergeometric Functions

被引：0

作者：

Ishkhanyan, T. A. ^{[1
]}

Ishkhanyan, A. M. ^{[1
]}

Cesarano, C. ^{[2
]}

机构：

[1] Inst Phys Res, Ashtarak 0204, Armenia

[2] Int Telemat Univ Uninettuno, I-00186 Rome, Italy

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2023年 / 44卷 / 12期

关键词：

generalized Heun equation; hypergeometric function; recurrence relation; ORDINARY DIFFERENTIAL EQUATION; RECURSIVE ASSOCIATED LAGUERRE; SERIES;

D O I：

10.1134/S1995080223120156

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a confluent modification of the general Heun equation having three regular singular points and an irregular singularity of rank one at infinity. We show that this equation admits infinitely many solutions in terms of a single generalized confluent hypergeometric function. The solutions apply if two regular singularities have non-zero integer characteristic exponents and each of the two accessory parameters obeys a polynomial equation.

引用

页码：5258 / 5265

页数：8

共 50 条

[1] Solutions of a Confluent Modification of the General Heun Equation in Terms of Generalized Hypergeometric Functions
T. A. Ishkhanyan
A. M. Ishkhanyan
C. Cesarano
Lobachevskii Journal of Mathematics, 2023, 44 : 5258 - 5265
[2] Expansions of the solutions to the confluent Heun equation in terms of the Kummer confluent hypergeometric functions
Ishkhanyan, T. A.
Ishkhanyan, A. M.
AIP ADVANCES, 2014, 4 (08):
[3] Generalized confluent hypergeometric solutions of the Heun confluent equation
Ishkhanyan, T. A.
Ishkhanyan, A. M.
APPLIED MATHEMATICS AND COMPUTATION, 2018, 338 : 624 - 630
[4] Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions
Leroy, C.
Ishkhanyan, A. M.
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2015, 26 (06) : 451 - 459
[5] Confluent Heun Equation and Confluent Hypergeometric Equation
Slavyanov S.Y.
Salatich A.A.
Journal of Mathematical Sciences, 2018, 232 (2) : 157 - 163
[6] Solutions of the bi-confluent Heun equation in terms of the Hermite functions
Ishkhanyan, T. A.
Ishkhanyan, A. M.
ANNALS OF PHYSICS, 2017, 383 : 79 - 91
[7] Generalized Hypergeometric Solutions of the Heun Equation
Ishkhanyan, A. M.
THEORETICAL AND MATHEMATICAL PHYSICS, 2020, 202 (01) : 1 - 10
[8] Generalized Hypergeometric Solutions of the Heun Equation
A. M. Ishkhanyan
Theoretical and Mathematical Physics, 2020, 202 : 1 - 10
[9] A note on the generalized-hypergeometric solutions of general and single-confluent Heun equations
Melikdzhanian, D. Yu
Ishkhanyan, A. M.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 499 (02)
[10] Generalized-hypergeometric solutions of the biconfluent Heun equation
D. Yu. Melikdzhanian
A. M. Ishkhanyan
The Ramanujan Journal, 2022, 57 : 37 - 53

← 1 2 3 4 5 →