Journal ArticleDOI
A method for computing Bessel function integrals
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TLDR
In this article, a method for numerical calculation of integrals containing Bessel functions of integer or integer plus one-half order is described, which involves first a one-dimensional Fourier sine or cosine transform followed by evaluation of the coefficient of the Chebyshev series of the Fourier-transformed function in the case of the Bessel function.About:
This article is published in Journal of Computational Physics.The article was published on 1988-04-01. It has received 15 citations till now. The article focuses on the topics: Bessel polynomials & Struve function.read more
Citations
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Journal ArticleDOI
Fast integration of rapidly oscillatory functions
TL;DR: In this paper, a collocation method for approximating integrals of rapidly oscillatory functions is presented, which is efficient for integrals involving Bessel functions Jv(rx) with large oscillation parameter r.
Numerical evaluation of special functions
Daniel W. Lozier,Walter Gautschi +1 more
TL;DR: The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of higher transcendental functions, and to offer some suggestions for future developments in this field.
Journal ArticleDOI
Numerical quadrature for Bessel transformations
TL;DR: In this paper, higher order numerical quadratures for the integration of systems containing Bessel functions are presented. But they are based on a truncation of the asymptotic series and extend an approach in the work of Levin.
Journal ArticleDOI
On the evaluation of Bessel transformations with the oscillators via asymptotic series of Whittaker functions
TL;DR: The integrals are transformed into the problems involving the complex exponential functions, which can be efficiently computed by using the complex integration method, and the entirely different asymptotic expansions from the references are obtained.
Book ChapterDOI
Numerical Integration of Highly Oscillating Functions
TL;DR: Some specific nonstandard methods for numerical integration of highly oscillating functions, mainly based on some contour integration methods and applications of some kinds of Gaussian quadratures, including complex oscillatory weights, are presented in this paper.
References
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Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Journal ArticleDOI
Methods of Numerical Integration.
The fast Fourier Transform
TL;DR: A computer algorithm that computes the discrete Fourier transform much faster than other algorithms, is explained and examples and detailed procedures are provided to assist the reader in learning how to use the algorithm.
Journal ArticleDOI
The optimum addition of points to quadrature formulae.
TL;DR: In this article, a new set of n-point Gauss, Lobatto and general quadrature formulae of degree 3n - 3 (n even) or 3n- 2 (n odd) is derived.
Related Papers (5)
Modified clenshaw-curtis method for the computation of Bessel function integrals
Robert Piessens,Maria Branders +1 more