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Bessel transforms and rational extrapolation. (English) Zbl 0554.65010
A numerical method is developed which handles the Bessel transform of functions having slow rates of decrease, i.e. f(u)=O(u -α ), u+ (α>0) in the Bessel transform H v (λ)= 0 f(u)J v (λu)du,v>-1/2· The method replaces H 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 v (λ) can be obtained from the damped transform by extrapolation with the Thiele algorithm.
MSC:
65D20Computation of special functions, construction of tables
65R10Integral transforms (numerical methods)
44A15Special transforms (Legendre, Hilbert, etc.)
44A20Integral transforms of special functions
33C10Bessel and Airy functions, cylinder functions, 0 F 1
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