The Complementary Hankel Type Transformations Of Arbitrary Order

In this paper four self-reciprocal integral transformations of Hankel type are defined. The simultaneous use of trans-formations H1,α,β and H2,α,β (which are denoted by Hα,β) allows us to solve many problems of Mathematical Physics involving the differential operator α,β= D2+4αx 1D, whereas the pair of transformations H3,α,β and H4,α,β (which we express by Hα,β) permits us to tackle those problems containing its adjoint operator, no matter what the real value of α β be. These transformations are also investigated in a space of generalized functions according to the mixed Parseval equation.