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Gauss quadrature approximations to hypergeometric and confluent hypergeometric functions. (English) Zbl 0998.65032
The author analyzes the error of the Gauss quadrature formula to compute hypergeometric and confluent hypergeometric functions based on their integral representations. The error is analyzed both in terms of the derivatives of the integrand and in terms of the derivative-free contour integral representation of the remainder term in the case of the confluent hypergeometric function. In the case of the hypergeometric function the analogous analyses of the error in terms of the derivative-free contour integral representation of the remainder term is given. These approaches lead to a priori estimates of the number of Gauss points needed for the given accuracy.
##### MSC:
 65D20 Computation of special functions, construction of tables 33C15 Confluent hypergeometric functions, Whittaker functions, ${}_{1}{F}_{1}$