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Elliptic Integrals

Elliptic integrals and Jacobian functions

MuPAD Functions

ellipticKComplete elliptic integral of the first kind
ellipticCKComplementary complete elliptic integral of the first kind
ellipticFIncomplete elliptic integral of the first kind
ellipticEComplete and incomplete elliptic integrals of the second kind
ellipticCEComplementary complete elliptic integral of the second kind
ellipticPiComplete and incomplete elliptic integrals of the third kind
ellipticCPiComplementary complete elliptic integral of the third kind
ellipticNomeElliptic nome
jacobiAMJacobi amplitude function am
jacobiSNJacobi elliptic function sn
jacobiCNJacobi elliptic function cn
jacobiDNJacobi elliptic function dn
jacobiCDJacobi elliptic function cd
jacobiSDJacobi elliptic function sd
jacobiNDJacobi elliptic function nd
jacobiDCJacobi elliptic function dc
jacobiNCJacobi elliptic function nc
jacobiSCJacobi elliptic function sc
jacobiNSJacobi elliptic function ns
jacobiDSJacobi elliptic function ds
jacobiCSJacobi elliptic function cs
jacobiZetaJacobi Zeta function


Special Functions Available in MuPAD

The following MuPAD® functions represent the Dirac δ-distribution and the Heaviside (step) function.

Floating-Point Arguments and Function Sensitivity

Particular choices of parameters can reduce some special functions to simpler special functions, elementary functions, or numbers.

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