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Zbl 0554.65010
Lund, John
Bessel transforms and rational extrapolation. (English)
[J] Numer. Math. 47, 1-14 (1985). ISSN 0029-599X; ISSN 0945-3245/e

A numerical method is developed which handles the Bessel transform of functions having slow rates of decrease, i.e. $f(u)=O(u\sp{-\alpha})$, $u\to +\infty$ $(\alpha >0)$ in the Bessel transform $H\sb v(\lambda)=\int\sp{\infty}\sb{0}f(u)J\sb v(\lambda u)du,v>-1/2.$ The method replaces $H\sb v$ by a related damped transform for which the sinc quadrature rule provides an efficient and accurate approximation. It is then shown that the value of $H\sb v(\lambda)$ can be obtained from the damped transform by extrapolation with the Thiele algorithm.

MSC 2000:: *65D20 Computation of special functions
65R10 Integral transforms (numerical methods)
44A15 Special transforms
44A20 Integral transforms of special functions
33C10 Cylinder functions, etc.

Keywords: rational extrapolation; Bessel transform; sinc quadrature; Thiele algorithm

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