The file EllipticIntegrals.mth defines functions for approximating elliptic integrals.  These integrals are described in Chapter 17 of Abramowitz and Stegun [1965].  See the introduction to ExponentialIntegrals.mth7RN4D for a discussion of accuracy.  The function definitions in the file are automatically loaded when any of its functions are first used.


ELLIPTIC_F(Φ, m) approximates to the elliptic integral of the first kind F(Φ|m).


ELLIPTIC_E(Φ, m) approximates to the elliptic integral of the second kind E(Φ|m).


ELLIPTIC_PI(Φ, m, n) approximates to the elliptic integral of the third kind II(n;Φ|m).


JACOBI_AM(u,m,n) is the Jacobi elliptic amplitude function needed to generate all the Jacobi elliptic functions.


KI(m,n) is the complete elliptic integral of the first kind.


EIF(Φ,m,n) is the elliptic integral of the first kind.


Other Utility File LibraryG5BS2R 

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