Fourier-Bessel series

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The expansion of a function in a series


where is a function given on the interval , is the Bessel function of order (cf. Bessel functions), and the are the positive zeros of taken in increasing order; the coefficients have the following values:

If is a piecewise-continuous function given on an interval and if the integral

then the Fourier–Bessel series converges and its sum is equal to at each interior point of at which locally has bounded variation.

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Fourier–Bessel series. Encyclopedia of Mathematics. URL: