The file HypergeometricFunctions.mth defines functions for approximating hypergeometric functions.  These functions are described in Chapters 13 and 15 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.


HYPERGEOMETRIC_SERIES(plist, qlist, z, m) simplifies to m+1 terms of the hypergeometirc series for the generalized hypergeometric function pFq(a1,...,ap;b1,...,bq;z) where plist equals [a1,...,ap] and qlist equals [b1,...,bq].


KUMMER(a, b, z) approximates to Kummer's function M(a, b, z) which is the solution of Kummer’s second order differential equation z·w’’ + (b-z)·w’ - a·w = 0.  M(a, b, z) equals the confluent hypergeometric function 1F1(a; b; z).


KUMMER_SERIES(a, b, z, m) simplifies to m+1 terms of the hypergeometric series for Kummer’s function.


GAUSS(a, b, c, z) approximates to the Gauss function F(a, b; c; z) which equals the hypergeometric function 2F1(a, b; c; z).


GAUSS_SERIES(a, b, c, z, m) simplifies to m+1 terms of the hypergeometric series for the Gauss function.


Other Utility File LibraryG5BS2R 

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