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Hankel transform
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==== Fourier transform in {{math|''d''}} dimensions (radially symmetric case) ==== If a {{math|''d''}}-dimensional function {{math|''f''(''r'')}} does not depend on angular coordinates, then its {{math|''d''}}-dimensional Fourier transform {{math|''F''(''k'')}} also does not depend on angular coordinates and is given by<ref>{{cite web|url=http://math.arizona.edu/~faris/methodsweb/hankel.pdf|title=Radial functions and the Fourier transform: Notes for Math 583A, Fall 2008|last=Faris|first=William G.|date=2008-12-06|website=University of Arizona, Department of Mathematics|accessdate=2015-04-25}}</ref><math display="block">k^{d/2-1}F(k) = (2 \pi)^{d/2} \int_{0}^{+\infty}r^{d/2-1}f(r)J_{d/2-1}(kr)r\mathrm{d}r.</math>which is the Hankel transform of <math>r^{d/2-1}f(r)</math> of order <math display="inline">(d/2-1)</math> up to a factor of <math>(2 \pi)^{d/2} </math>.
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