Special functions arise in many problems of pure and applied mathematics, mathematical statistics, physics, and engineering. This book provides an overview of numerical methods for computing special functions and discusses when to use these methods depending on the function and the range of parameters. It considers not only standard and simple parameter domains, but also describes methods valid for large and complex parameters. While its focus is on the computation of special functions, it is also suitable for general numerical analysis courses. The authors provide pseudoalgorithms to help students write their own algorithms, and also discuss other useful and efficient methods, such as methods for computing zeros of special functions, uniform asymptotic expansions and Pade approximations. It also includes specific algorithms for computing several special functions. Intended for researchers in applied mathematics, scientific computing, physics, engineering, statistics, and other scientific disciplines in which special functions are used as computational tools.
Amparo Gil is an Associate Professor of Applied Mathematics at the Universidad de Cantabria in Spain. Javier Segura is an Associate Professor of Mathematical Analysis at the Universidad de Cantabria in Spain. Nico M. Temme is a guest researcher at the 'Centrum voor Wiskunde en Informatica' (CWI) in Amsterdam, since his retirement in 2005.