- 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).

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

[Next: ellipticE] [Last: ellipticNome] [Top] |

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] |

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] |

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] |

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

[Next: ellipticCK] [Previous: ellipticF] [Top] |

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] |

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] |

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] |

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] |

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] |

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] |