Fourier-Bessel series
From Encyclopedia of Mathematics
The expansion of a function in a series
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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:
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If is a piecewise-continuous function given on an interval
and if the integral
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then the Fourier–Bessel series converges and its sum is equal to at each interior point
of
at which
locally has bounded variation.
How to Cite This Entry:
Fourier-Bessel series. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fourier-Bessel_series&oldid=19087
Fourier-Bessel series. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fourier-Bessel_series&oldid=19087
This article was adapted from an original article by L.N. Karmazina (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article