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The solution of Bessel function dual integral equations by a multiplying-factor method

Published online by Cambridge University Press:  24 October 2008

B. Noble
B. Noble
Affiliation:
Department of Mathematics, The Royal College of Science and Technology, Glasgow
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Extract

In this paper we first of all consider the dual integral equations

where f(ρ), g(ρ) are given, A(t) is unknown, and α is a given constant. This system, with g(ρ) = 0, was originally considered by Titchmarsh ((13), p. 337), and Busbridge (1), who obtained a solution by the use of Mellin transforms and analytic continuation in the complex plane. The method described in this paper involves the application of certain multiplying factors to the equations. In the present case it is relatively easy to guess the multiplying factors and then the method is essentially a real-variable technique. It is presented in this way in § 2 below.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 2 , April 1963 , pp. 351 - 362
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

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