International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 2, Pages 323-332
Hankel complementary integral transformations of arbitrary order
1Departamento de Informática y Sistemas, Universidad de Las Palmas, Canary Islands, Las Palmas de Gran Canaria, Spain
2Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de La Laguna, Tenerife, Canary Islands, La Laguna, Spain
Received 13 November 1990; Revised 18 June 1991
Copyright © 1992 M. Linares Linares and J. M. R. Mendez Pérez. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Four selfreciprocal integral transformations of Hankel type are defined throughwhere ; ; , , being the Bessel function of the first kind of order ; , ; , , and , . The simultaneous use of transformations , and , (which are denoted by ) allows us to solve many problems of Mathematical Physics involving the differential operator , whereas the pair of transformations and , (which we express by ) permits us to tackle those problems containing its adjoint operator , no matter what the real value of be. These transformations are also investigated in a space of generalized functions according to the mixed Parseval equationwhich is now valid for all real .