Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-05T02:55:56.445Z Has data issue: false hasContentIssue false

A self-reciprocal function

Published online by Cambridge University Press:  20 January 2009

Brij Mohan
Affiliation:
Benares Hindu University, India.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
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.).