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On a function which is self-reciprocal in the Hankel transform

Published online by Cambridge University Press:  20 January 2009

E. G. Phillips
E. G. Phillips
Affiliation:
(University College of North Wales, Bangor).
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It is well-known that if v≧–½ and

then ø (x) is said to be self-reciprocal in the Hankel transform and may be described as Rv. If v = ±½(1) reduces to the Fourier sine or cosine transform. Functions of these two classes may be described as Rg and Re.

In a list of pairs of reciprocal functions, G. A. Campbell gives the example that

is Rc, but there does not seem to be any explicit reference to this function in the literature. It suggests that there is a corresponding function which is Rv.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 5 , Issue 1 , October 1936 , pp. 35 - 36
Copyright
Copyright © Edinburgh Mathematical Society 1936

References

page 35 note 1 Bell System Technical Journal, 7 (1928).Google Scholar

page 35 note 2 Watson, , Bessel Functions, §13·47 (2), 416.Google Scholar

page 35 note 3 Quarterly Journal of Math., (Oxford Series) 1 (1930), 208.Google Scholar

page 36 note 1 See Watson, , Bessel Functions §13·47 (6), 417.Google Scholar

page 36 note 2 Loc, cit., 211.Google Scholar