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Zbl 0574.65013
Lyness, J.N.
Integrating some infinite oscillating tails. (English)
[J] J. Comput. Appl. Math. 12/13, 109-117 (1985). ISSN 0377-0427

In numerical integration of a slowly decaying function f(x) with alternative sign, the tail of f(x) is often expressed as $f(x)=g(x)j(x)$, where j(x) is a Bessel function $J\sb 0(x)$ or $J\sb 1(x)$ and g(x) is a ultimately positive function. For making it easier to calculate, this proposal approximates the consecutive zeros of the Bessel function by $J\sb 1(x)\approx \sqrt{2/\pi x}(\cos (x-(3/4)\pi)).$
[Y.Kobayashi]

MSC 2000:: *65D32 Quadrature formulas (numerical methods)
42A16 Fourier coefficients, etc.

Keywords: Euler transformation; oscillatory integrals; trigonometric approximation; Bessel function

Cited in: Zbl 0811.65017 Zbl 0589.65018

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