Automatic Computing Methods for Special Functions. Part IV. Complex Error Function, Fresnel Integrals, and Other Related Functions

Computing Integrals of Highly Oscillatory Special Functions Using Complex Integration Methods and Gaussian Quadratures

An account on computation of integrals of highly oscillatory functions based on the so-called complex integration methods is presented. Beside the basic idea of this approach some applications in computation of Fourier and Bessel transformations are given. Also, Gaussian quadrature formulas with a modified Hermite weight are considered, including some numerical examples.

An error analysis of two related quadrature methods for computing zeros of analytic functions, Part II

We consider the quadrature method developed by Kravanja, Sakurai and Van Barel (BIT 39 (1999), no. 4, 646–682) for computing all the zeros of an analytic function that lie inside the unit circle. A new perturbation result for generalized eigenvalue problems allows us to obtain a detailed upper bound for the error between the zeros and their approximations. To the best of our knowledge, it is th...

On High Precision Methods for Computing Integrals Involving Bessel Functions

The technique of Bakhvalov and Vasil'eva for evaluating Fourier integrals is generalized to integrals involving exponential and Bessel functions.

On High Precision Methods for Computing Integrals of Oscillatory Functions*

A short account of the most important methods for the evaluation of integrals of oscillatory functions and an unified approach for such a purpose are given.

Numerical methods for special functions