New indefinite integrals of Heun functions

被引：2

作者：

Batic, D. ^{[1
]}

Forrest, O. ^{[2
]}

Nowakowski, M. ^{[3
]}

机构：

[1] Khalifa Univ Sci & Technol, Dept Math, Main Campus, Abu Dhabi, U Arab Emirates

[2] Univ West Indies, Dept Math, Kingston, Jamaica

[3] Univ los Andes, Dept Phys, Bogota, Colombia

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2018年 / 29卷 / 10期

关键词：

Special functions; Heun functions; hypergeometric functions; complete elliptic integrals;

D O I：

10.1080/10652469.2018.1499021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a conspicuous number of indefinite integrals involving Heun functions and their products obtained by means of the Lagrangian formulation of a general homogeneous linear ordinary differential equation. As a by-product we also derive new indefinite integrals involving the Gauss hypergeometric function and products of hypergeometric functions with elliptic functions of the first kind. All integrals we obtained cannot be computed using Maple and Mathematica.

引用

页码：794 / 804

页数：11

共 7 条

[1]

[Anonymous], 1995, Heun's Differential Equations

[2]

[Anonymous], 1964, Handbook of mathematical functions with formulas, graphs, and mathematical tables

[3]

Conway JT., 2015, INTEGRAL TRANSFORMS, V26, P1, DOI [10.1080/10652469.2014.956311, DOI 10.1080/10652469.2014.956311]

[4] About derivatives of Heun's functions from polynomial transformations of hypergeometric equations [J].

Hounkonnou, Mahouton Norbert ;

Ronveaux, Andre .

APPLIED MATHEMATICS AND COMPUTATION, 2009, 209 (02) :421-424

[5]

Jeffrey A., 2007, Table of integrals, series, and products

[6] On reducing the Heun equation to the hypergeometric equation [J].

Maier, RS .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 213 (01) :171-203

[7]

Prudnikov A. P., 1990, INTEGRALS AND SERIES, V3

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