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A self-reciprocal function

Published online by Cambridge University Press:  20 January 2009

Brij Mohan
Brij Mohan
Affiliation:
Benares Hindu University, India.
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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

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 6 , Issue 2 , October 1939 , pp. 92 - 93
Copyright
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.).