Indefinite integrals involving the incomplete elliptic integrals of the first and second kinds

被引：5

作者：

Conway, John T. ^{[1
]}

机构：

[1] Univ Agder, Dept Sci & Engn, Grimstad, Norway

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2016年 / 27卷 / 05期

关键词：

differential equations; elliptic integrals; Euler-Lagrange; 70H03; 33E05; 34A30;

D O I：

10.1080/10652469.2015.1132715

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A substantial number of indefinite integrals are presented for the incomplete elliptic integrals of the first and second kinds. The number of new results presented is about three times the total number to be found in the current literature. These integrals were obtained with a Lagrangian method based on the differential equations which these functions obey. All results have been checked numerically with Mathematica. Similar results for the incomplete elliptic integral of the third kind will be presented separately.

引用

页码：371 / 384

页数：14

共 7 条

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[Anonymous], 2000, The mathematica book

[2]

Byrd P., 1971, Grundlehren der mathematischen Wissenschaften

[3] A Lagrangian method for deriving new indefinite integrals of special functions [J].

Conway, John T. .

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2015, 26 (10) :812-824

[4]

Conway JT, 2015, INTEGRAL TRANSFORMS

[5]

Conway JT, 2015, INTEGRAL TRANSFORMS, DOI [10.1080/106352469.2015.1063627, DOI 10.1080/106352469.2015.1063627]

[6]

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

[7]

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

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