Automatic computing methods for special functions. Part III. The sine, cosine, exponential integrals, and related functions

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.

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.

Several Differentiation Formulas of Special Functions. Part III

The articles [13], [15], [16], [1], [4], [10], [11], [17], [5], [14], [12], [2], [6], [9], [7], [8], and [3] provide the terminology and notation for this paper. For simplicity, we follow the rules: x, r, a, b denote real numbers, n denotes a natural number, Z denotes an open subset of R, and f , f1, f2, f3 denote partial functions from R to R. One can prove the following propositions: (1) x2 Z...

Numerical methods for special functions