This paper describes methods that are important for the numerical evaluation of certain functions that frequently occur in applied mathematics, physics and mathematical statistics. This includes what we consider to be the basic methods, such as recurrence relations, series expansions (both convergent and asymptotic), and numerical quadrature. Several other methods are available and some of these will be discussed in less detail. Examples will be given on the use of special functions in certain problems from mathematical physics and mathematical statistics (integrals and series with special functions).

computaion of special functions
Computation of special functions, construction of tables (msc 65D20)
Cambridge University Press
Acta Numerica

Temme, N.M. (2007). Numerical aspects of special functions. Acta Numerica, 16, 379–478.