6533b7d4fe1ef96bd1262663

RESEARCH PRODUCT

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

John T. Conway

subject

Abelian integralCarlson symmetric formQuarter periodApplied Mathematics010102 general mathematicsMathematical analysisTrigonometric integral010103 numerical & computational mathematics01 natural sciencesJacobi elliptic functionsLegendre formSlater integralsElliptic integral0101 mathematicsAnalysisMathematics

description

ABSTRACTA 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.

yearjournalcountryeditionlanguage
2016-01-19Integral Transforms and Special Functions
https://doi.org/10.1080/10652469.2015.1132715