International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 417-427

On a non-self adjoint expansion formula

D. Naylor

Department of Applied Mathematics, The University of Western Ontario, London N6A 5B9, Ontario, Canada

Received 4 May 1984

Copyright © 1984 D. Naylor. 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.


This paper develops a formula of inversion for an integral transform of the kind similar to that associated with the names of Kontorovich and Lebedev except that the kernel involves the Neumann function Yu(kr) and the variable r varies over the infinite interval ar< where a>0 The transform is useful in the investigation of functions that satisfy the Helmholtz equation and a condition of radiation at infinity. The formula established is expressed entirely in terms of series expansions and replaces earlier inversion formulas that require the evaluation of contour integrals.