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I am dealing with the following problem. Solving and kinetic equation I came up with the expression

H_1^(-1)[H_0(P(r))/q]

where H_0 is the zero order Hankel transform, H_1^(-1) is the first order inverse Hankel transform P(r) is a function that depends on the radial coordinate in cylindrical symmetry. q is the variable of the transformation that comes from the definitions of the respective Bessel functions J_0(q*r) and J_1(q*r).

My question is is there a way to analytically take an inverse first order Hankel transform of a zero order Hankle transform of the function P(r). I have been through a lot of literature but could not find any discussion. On the other hand such expression seems to occeru pretty commonly when dealing with the radial part of cylindrical divergence.

Thanks in advance for any help

dnp

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# Zero and first order Hankel Transforms

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