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.
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页码：371 / 384
页数：14
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