This paper gives an overview of methods for the numerical evaluation of special functions, that is, the functions that arise in many problems from mathematical physics, engineering, probability theory, and other applied sciences. We consider in detail a selection of basic methods which are frequently used in the numerical evaluation of special functions: converging and asymptotic series, including Chebyshev expansions, linear recurrence relations, and numerical quadrature. Several other methods are available and some of these will be discussed in less detail. We give examples of recent software for special functions where these methods are used. We mention a list of new publications on computational aspects of special functions available on our website.

Additional Metadata
Keywords numerical evaluation of special functions, Chebyshev expansions, quadrature methods, transformation of series, continued fractions, asymptotic analysis
MSC Computation of special functions, construction of tables (msc 65D20)
Publisher Springer
Editor T.E. Simos
Citation
Gil, A, Segura, J, & Temme, N.M. (2011). Basic Methods for Computing Special Functions. In T.E Simos (Ed.), Recent Advances in Computational and Applied Mathematics. Springer.