On a non-self adjoint expansion formula

D. Naylor

International Journal of Mathematics and Mathematical Sciences, 1984, vol. 7, 1-11

Abstract:

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 Y u ( k r ) and the variable r varies over the infinite interval a ≤ r < ∞ 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.

Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:926176

DOI: 10.1155/S0161171284000454

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