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XIV.—Dual Series Relations. I. Dual Relations Involving Fourier-Bessel Series*

Published online by Cambridge University Press:  14 February 2012

I. N. Sneddon  and
R. P. Srivastav
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Synopsis

The solution of the dual series relations

where {λn) is the sequence of positive zeros of the Bessel function Jν(αλ), arranged in order of increasing magnitude, þ and ν are real numbers (−1 <þ < 1, ν >0), the functions, f1(ρ), f2(ρ) being prescribed, is obtained by giving an integral representation of {αn} in terms of a single function g(t). The problem is reduced to that of solving a Fredholm integral equation of the second kind for the auxiliary function g(t).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 66 , Issue 3 , 1963 , pp. 150 - 160
Copyright
Copyright © Royal Society of Edinburgh 1963

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References

References to Literature

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