New indefinite integrals of Heun functions

D. Batic; O. Forrest; M. Nowakowski

doi:10.1080/10652469.2018.1499021

New indefinite integrals of Heun functions

D. Batic, O. Forrest, M. Nowakowski

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	British English
Pages (from-to)	794-804
Number of pages	11
Journal	Integral Transforms and Special Functions
Volume	29
Issue number	10
DOIs	https://doi.org/10.1080/10652469.2018.1499021
State	Published - 3 Oct 2018

Keywords

33C05
33C55
33E05
33E99
34A99
70H03
complete elliptic integrals
Heun functions
hypergeometric functions
Special functions

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10.1080/10652469.2018.1499021

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abstract = "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.",

keywords = "33C05, 33C55, 33E05, 33E99, 34A99, 70H03, complete elliptic integrals, Heun functions, hypergeometric functions, Special functions",

author = "D. Batic and O. Forrest and M. Nowakowski",

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T1 - New indefinite integrals of Heun functions

AU - Batic, D.

AU - Forrest, O.

AU - Nowakowski, M.

PY - 2018/10/3

Y1 - 2018/10/3

N2 - 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.

AB - 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.

KW - 33C05

KW - 33C55

KW - 33E05

KW - 33E99

KW - 34A99

KW - 70H03

KW - complete elliptic integrals

KW - Heun functions

KW - hypergeometric functions

KW - Special functions

UR - http://www.scopus.com/inward/record.url?scp=85050350561&partnerID=8YFLogxK

U2 - 10.1080/10652469.2018.1499021

DO - 10.1080/10652469.2018.1499021

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SN - 1065-2469

VL - 29

SP - 794

EP - 804

JO - Integral Transforms and Special Functions

JF - Integral Transforms and Special Functions

IS - 10

ER -

New indefinite integrals of Heun functions

Abstract

Keywords

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