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Parseval's integral and the Jacobi expansions in series of Bessel fuinctions
Published online by Cambridge University Press: 17 February 2009
Abstract
The sums
are shown to approximate J0 (z); the error terms are series in higher order Bessel functions, leading with J2M (z). Similar sums approximate J1(z). These sums may be looked on as extensions of the Jacobi expansions for cos z and sin z in series of Bessel functions. They become numerically useful for M > |z|.
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- Copyright © Australian Mathematical Society 1986