Numerical aspects of special functions

Numerical Evaluation of Special Functions

Higher transcendental functions continue to play varied and important roles in investigations by engineers, mathematicians, scientists and statisticians. The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of these functions, and to offer some suggestions for future developments in this field. March 1994 December 200

Numerical methods for special functions

The spiral of Theodorus, numerical analysis, and special functions

Numerical and Asymptotic Aspects of Parabolic Cylinder Functions

Several uniform asymptotics expansions of the Weber parabolic cylinder functions are considered, one group in terms of elementary functions, another group in terms of Airy functions. Starting point for the discussion are asymptotic expansions given earlier by F.W.J. Olver. Some of his results are modified to improve the asymptotic properties and to enlarge the intervals for using the expansions...

Orthogonal rational functions for system identification: numerical aspects

Recently, there has been a growing interest in the use of orthogonal rational functions (ORFs) in system identification. There are many advantages over more classical techniques. Probably due to a known explicit expression for the basis functions when the orthogonality weight is uniformly equal to 1 (the so called Malmquist basis), the attention has been on the development of methods using this...