6533b833fe1ef96bd129b596
RESEARCH PRODUCT
Indefinite integrals involving the Jacobi Zeta and Heuman Lambda functions
John T. Conwaysubject
Carlson symmetric formPure mathematicsQuarter periodApplied Mathematics010102 general mathematicsMathematical analysisElliptic functionTrigonometric integral010103 numerical & computational mathematics01 natural sciencesJacobi elliptic functionsLegendre formElliptic rational functionsElliptic integral0101 mathematicsAnalysisMathematicsdescription
ABSTRACTJacobian elliptic functions are used to obtain formulas for deriving indefinite integrals for the Jacobi Zeta function and Heuman's Lambda function. Only sample results are presented, mostly obtained from powers of the twelve Glaisher elliptic functions. However, this sample includes all such integrals in the literature, together with many new integrals. The method used is based on the differential equations obeyed by these functions when the independent variable is the argument u of elliptic function theory. The same method was used recently, in a companion paper, to derive similar integrals for the three canonical incomplete elliptic integrals.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-05-23 | Integral Transforms and Special Functions |