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

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