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A self-reciprocal function
Published online by Cambridge University Press: 20 January 2009
Extract
1. The object of this note is to discover a new function which is its own reciprocal in the Hankel Transform of order zero.
I will make use of the following theorem of Hardy and Titchmarsh1:–
A necessary and sufficient condition that a Junction f (x) should be its own Jv transform is that it should be of the form
where 0 < c < 1, and
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- Research Article
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- Copyright © Edinburgh Mathematical Society 1939
References
1 Titchmarsh, E. C.: The Theory of the Fourier Integral (Oxford, 1937), §(9.1.9.).Google Scholar
2 Ibid., §(7.10.8.).