ALGORITHMS FOR RATIONAL APPROXIMATIONS FOR THE GAUSSIAN HYPERGEOMETRIC FUNCTION

In previous studies, rational approximations for 2F1 (a, b;c;-z) were examined in some detail. If a=1, complete a priori error analyses for the main diagonal Pade approximations and much more were presented. For general parameters, the rational approximations are not of the Pade class. It was shown that they converge, but a complete error description was not available. This deficiency is now corrected. Further, FORTRAN programs are available to evaluate the rational approximations by using the appropriate recursion formulas to generate the numerator and denominator polynomials as a number, and to also evaluate the coefficients which define these polynomials.