Numerical Methods for Special Functions
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Author(s): A. Gil, J. Segura and N. Temme
Publisher: SIAM
ISBN: 9780898716344
Format: softback
417pp
Price: $99.00
Review Date: 24 March 2008
Review: Special functions are referred to as mathematical functions which are widely used in scientific and technical applications. The main purpose of the book is to provide a guide to computational methods and when to use them. The book contains examples to illustrate the methods and most of the chapters start from basic principles. The book is in four parts. The first is called basic methods and covers methods which in the authors’ experience are the most popular and important ones for special functions. It covers convergent and divergent series, Chebyshev, linear recurrence relations and quadrature methods. The second part called tools and methods contains important methods which are not so well known, such as uniform asymptotic expansions, continued fractions, computation of zeros of special functions. The third part called related topics and examples covers methods which are specific to certain functions, such as numerical inversion, Euler summation formula and computation fo symmetric elliptic integrals and numerical inversion of Laplace transforms. The fourth part covers Airy functions, Legendre functions and parabolic functions among others. Fortran 90 rountines are downloadable from a given website.