Numerical Aspects of Special Functions

Abstract

C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c a Modelling, Analysis and Simulation Modelling, Analysis and SimulationNumerical aspects of special functions N.M. Temme Numerical aspects of special functions ABSTRACT 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). REPORT MAS-E0711 JULY 2007 Mathematics Subject Classification: 65D20