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Hankel transform
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===Domain of definition=== Inverting a Hankel transform of a function ''f''(''r'') is valid at every point at which ''f''(''r'') is continuous, provided that the function is defined in (0, β), is piecewise continuous and of [[bounded variation]] in every finite subinterval in (0, β), and : <math>\int_0^\infty |f(r)|\,r^{\frac{1}{2}} \,\mathrm{d}r < \infty.</math> However, like the Fourier transform, the domain can be extended by a density argument to include some functions whose above integral is not finite, for example <math>f(r) = (1 + r)^{-3/2}</math>.
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