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On a non-self adjoint expansion formula

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  • D. Naylor

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.

Suggested Citation

  • D. Naylor, 1984. "On a non-self adjoint expansion formula," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 7, pages 1-11, January.
    • Handle: RePEc:hin:jijmms:926176
    DOI: 10.1155/S0161171284000454
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