Collected works

This Book Gives An Introduction To The Classical, Well-known Special Functions Which Play A Role In Mathematical Physics, Especially In Boundary Value Problems. Calculus And Complex Function Theory Form The Basis Of The Book And Numerous Formulas Are Given. Particular Attention Is Given To Asymptomatic And Numerical Aspects Of Special Functions, With Numerous References To Recent Literature Provided. Bernoulli, Euler And Stirling Numbers -- Useful Methods And Techniques -- The Gamma Function -- Differential Equations -- Hypergeometric Functions -- Orthogonal Polynomials -- Confluent Hypergeometric Functions -- Legendre Functions -- Bessel Functions -- Separating The Wave Equation -- Special Statistical Distribution Functions -- Elliptic Integrals And Elliptic Functions -- Numerical Aspects Of Special Functions. Nico M. Temme. Includes Bibliographical References And Index.

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 Padé 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.

The author provides an introduction to the classical well-known special functions which play a role in mathematical physics, especially in boundary value problems. Written for students and researchers in mathematics, physics, and engineering who encounter special functions in their work and for whom the results are too scattered in the general literature. Includes scores of exercises and notations at the end of every chapter. This work 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