6533b837fe1ef96bd12a2ffe
RESEARCH PRODUCT
Indefinite integrals involving complete elliptic integrals of the third kind
John T. Conwaysubject
Carlson symmetric formAbelian integralPure mathematicsApplied MathematicsMultiple integral010102 general mathematicsMathematical analysisSurface integralLine integralTrigonometric integral010103 numerical & computational mathematicsDarboux integral01 natural sciencesVolume integral0101 mathematicsAnalysisMathematicsdescription
ABSTRACTA method developed recently for obtaining indefinite integrals of functions obeying inhomogeneous second-order linear differential equations has been applied to obtain integrals with respect to the modulus of the complete elliptic integral of the third kind. A formula is derived which gives an integral involving the complete integral of the third kind for every known integral for the complete elliptic integral of the second kind. The formula requires only differentiation and can therefore be applied for any such integral, and it is applied here to almost all such integrals given in the literature. Some additional integrals are derived using the recurrence relations for the complete elliptic integrals. This gives a total of 27 integrals for the complete integral of the third kind, including the single integral given in the literature. Some typographical errors in a previous related paper are corrected.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-04-13 | Integral Transforms and Special Functions |