On High Precision Methods for Computing Integrals Involving Bessel Functions
نویسندگان
چکیده
The technique of Bakhvalov and Vasil'eva for evaluating Fourier integrals is generalized to integrals involving exponential and Bessel functions.
منابع مشابه
A Method for Computing Bessel Function Integrals
Infinite integrals involving Bessel functions are recast, by means of an Abel transform, in terms of Fourier integrals. As there are many efficient numerical methods for computing Fourier integrals, this leads to a convenient way of approximating Bessel function integrals.
متن کاملComputing hypergeometric functions rigorously
We present an efficient implementation of hypergeometric functions in arbitraryprecision interval arithmetic. The functions 0F1, 1F1, 2F1 and 2F0 (or the Kummer U -function) are supported for unrestricted complex parameters and argument, and by extension, we cover exponential and trigonometric integrals, error functions, Fresnel integrals, incomplete gamma and beta functions, Bessel functions, ...
متن کاملAn Automatic Integration of Infinite Range Integrals Involving Bessel Functions
An efficient automatic quadrature procedure is developed for numerically computing the integrals 0 , where the function is smooth and nonoscillatory at infinity and is the Bessel functions of order ν =1,0 and 1/4. The procedure involves the use of an automatic integration scheme of modified FFT used for evaluating Fourier integrals and product type integration, and the modified W-transformation...
متن کاملSome Integrals Involving Bessel Functions Some Integrals Involving Bessel Functions
A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized hypergeometric function with subsequent reduction to special cases. Connection is made with Weber's second exponential integral and Laplace transforms of pr...
متن کاملInequalities for Integrals of Modified Bessel Functions and Expressions Involving Them
Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases, we show that we obtain the best possible constant or that our bounds are tight in certain limits. We apply these inequalities to obtain uniform bounds for several expressions involving integrals of modified Bessel functions. Such expressions occur in Stein’...
متن کامل