Y and H transforms

In mathematics, the transforms and transforms are complementary pairs of integral transforms involving, respectively, the Neumann function (Bessel function of the second kind) of order and the Struve function of the same order.
For a given function , the -transform of order is given by
The inverse of above is the -transform of the same order; for a given function , the -transform of order is given by
These transforms are closely related to the Hankel transform, as both involve Bessel functions.
In problems of mathematical physics and applied mathematics, the Hankel, , transforms all may appear in problems having axial symmetry.
Hankel transforms are however much more commonly seen due to their connection with the 2-dimensional Fourier transform. The , transforms appear in situations with singular behaviour on the axis of symmetry (Rooney).