Y and H transforms
In mathematics, the Y transforms and H transforms are complementary pairs of integral transforms involving, respectively, the Neumann function (Bessel function of the second kind) Yν of order ν and the Struve function Hν of the same order. For a given function f(r), the Y-transform of order ν is given by F ( k ) = ∫ 0 ∞ f ( r ) Y ν ( k r ) k r d r {\displaystyle F(k)=\int _{0}^{\infty }f(r)Y_{\nu }(kr){\sqrt {kr}}\,dr} The inverse of above is the H-transform of the same order; for a given function F(k), the H-transform of order ν is given by f ( r ) = ∫ 0 ∞ F ( k ) H ν ( k r ) k r d k {\displaystyle f(r)=\int _{0}^{\infty }F(k)\mathbf {H} _{\nu }(kr){\sqrt {kr}}\,dk} These transforms are closely related to the Hankel transform, as both involve Bessel functions.