Van der Laan C.G., Temme N.M. Calculation of special functions: gamma function, exponential integrals, error-like functions

Amsterdam, 1986. — 243 p.The main scope of these notes is to review and to discuss several aspects of implementations for the numerical computation of special functions. In this tract we consider functions which are related to the Euler gamma function, the exponential integrals and the error functions. For each of these groups we give definitions, analytic properties and fundamental formulas; algorithms, implementations, error analysis, references to tabulated coefficients, and testing aspects.
The first two chapters contain general information on the computation of special functions. The first one gives an annotated introduction to the literature and to several program libraries. Some local program libraries are surveyed when sufficient information happened to be available to us. No systematic search is made in checking more Computer Centres. The second chapter gives a theoretical background on error analysis, recurrence relations, continued fractions and generalized hypergeometric functions.