Hankel Transform - Some Hankel Transform Pairs

Some Hankel Transform Pairs

for -2
, z may be any complex number

is a modified Bessel function of the second kind. The expression coincides with the expression for the Laplace operator in polar coordinates applied to a spherically symmetric function .

The Hankel transform of Zernike polynomials are essentially Bessel Functions (Noll 1976):

R_n^m(r)=(-1)^{(n-m)/2}\int_0^\infty J_{n+1}(k)J_m(kr)\operatorname{d}k

for even .

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