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Computing the hypergeometric function. (English) Zbl 0886.65009
The Gauss hypergeometric function ${}_2F_1(a,b;c;x)$ is computed for real values of the variables $a, b, c$ and $x$. Transformation formulas are used to give a suitable $x-$interval for the power series. Great care is taken for the divergences that occur for certain values of $a, b$ and $c$ in the transformations. Chebyshev expansions are used for gamma functions and for certain combinations of gamma functions. Details of a Fortran program are given.

65D20Computation of special functions, construction of tables
33C05Classical hypergeometric functions, ${}_2F_1$
33-04Machine computation, programs (special functions)
Full Text: DOI
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