Limits of Lipschitz-Hankel Integrals

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Abstract
This paper is concerned with the limit as ζ approaches zero of certain integrals of the type which are useful in applications. This limit is shown to exist in the sense of generalized functions for all values of the parameters m,n,p. A scheme for calculating the limit is developed and applied for several explicit values of the parameters. These calculations are extended in a number of directions to obtain general formulae for certain types of limits. The results are applied to two problems is mathematical physics. Two appendices give the elliptical integral representation and asymptotic expansion of these integrals.

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