OpenMath Content Dictionary: ellipticFns

Canonical URL:
http://www.openmath.org/CDs/ellipticFns.ocd
CD File:
ellipticFns.ocd
CD as XML Encoded OpenMath:
ellipticFns.omcd
Defines:
ellipticCE, ellipticCK, ellipticCPi, ellipticE, ellipticEinc, ellipticF, ellipticK, ellipticModulus, ellipticNome, ellipticPi, ellipticPiInc
Date:
2001-30-08
Version:
1
Review Date:
Status:
experimental

2002-01-01

This content dictionary contains symbols to describe the elliptic functions. They are defined as in Abromowitz and Stegun (ninth printing on).


ellipticEinc

This symbol represents the incomplete elliptic integral of the second kind, it takes two arguments and is defined by : ellipticEinc(z,k) = int(sqrt(1-k^2*t^2)/sqrt(1-t^2),t=0..z)

Signatures:
sts


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ellipticE

This symbol represents the complete elliptic integral of the second kind, it takes one argument and is defined by : ellipticE(z) = ellipticEinc(1,z)

Signatures:
sts


[Next: ellipticCE] [Previous: ellipticEinc] [Top]

ellipticCE

This symbol represents the complementary complete elliptic integral of the second kind, it takes one argument and is defined by : ellipticCE(k) = ellipticEinc(1,sqrt(1-k^2))

Signatures:
sts


[Next: ellipticF] [Previous: ellipticE] [Top]

ellipticF

This symbol represents the incomplete elliptic integral of the first kind, it takes two arguments and is defined by : ellipticF(z,k) = int(1/sqrt(1-t^2)/sqrt(1-k^2*t^2),t=0..z)

Signatures:
sts


[Next: ellipticK] [Previous: ellipticCE] [Top]

ellipticK

This symbol represents the complete elliptic integral of the first kind it takes one argument and is defined by: ellipticK(k) = ellipticF(1,k)

Signatures:
sts


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ellipticCK

This symbol represents the complementary complete elliptic integral of the first kind it takes one argument and is defined by: ellipticCK(k) = ellipticF(1,sqrt(1-k^2))

Signatures:
sts


[Next: ellipticPiInc] [Previous: ellipticK] [Top]

ellipticPiInc

This symbol represents the incomplete elliptic integral of the third kind it takes three arguments and is defined by: ellipticPiInc(z,nu,k) = int(1/(1-nu*t^2)/sqrt(1-t^2)/sqrt(1-k^2*t^2),t=0..z)

Signatures:
sts


[Next: ellipticPi] [Previous: ellipticCK] [Top]

ellipticPi

This symbol represents the complete elliptic integral of the third kind it takes two arguments and is defined by: ellipticPi(nu,k) = ellipticPiInc(1,nu,k)

Signatures:
sts


[Next: ellipticCPi] [Previous: ellipticPiInc] [Top]

ellipticCPi

This symbol represents the complementary complete elliptic integral of the third kind it takes two arguments and is defined by: ellipticCPi(nu,k) = ellipticPi(1,nu,sqrt(1-k^2))

Signatures:
sts


[Next: ellipticModulus] [Previous: ellipticPi] [Top]

ellipticModulus

This symbol represents the elliptic modulus function, it takes one argument and is defined by: ellipticModulus(q) = JacobiTheta2(0,q)^2/JacobiTheta3(0,q)^2

Signatures:
sts


[Next: ellipticNome] [Previous: ellipticCPi] [Top]

ellipticNome

This symbol represents the elliptic Nome function, it takes one argument and is defined by: ellipticNome(k) = E^(-Pi*ellipticCK(k)/ellipticK(k))

Signatures:
sts


[First: ellipticEinc] [Previous: ellipticModulus] [Top]