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Generalisation of an Integral due to Hardy

Published online by Cambridge University Press:  18 May 2009

Fouad M. Ragab
Fouad M. Ragab
Affiliation:
University of Glasgow
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§ 1. Introductory. The integral

where b>0, was given by Hardy (1). It was proved by applying Mellin's inversion formula. An alternative proof, based on the differential equation

satisfied by Kn(x), has been given by the author (2).

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 1 , Issue 3 , September 1953 , pp. 115 - 117
Copyright
Copyright © Glasgow Mathematical Journal Trust 1953

References

REFERENCES

(1)Hardy, G. H., Mess, of Maths., 56, 190 (1927).Google Scholar
(2)Ragab, F. M., Proc. Glasg. Math. Ass., 1, 72 (1952).CrossRefGoogle Scholar
(3)Gray, , Mathews, and MacRobert, , Bessel Functions, p. 66.Google Scholar
(4)MacRobert, T. M., Complex Variable, p. 154.Google Scholar
(5)Watson, G. N., Bessel Functions, p. 437.Google Scholar
(6)MacRobert, T. M., Complex Variable (3rd ed.), p. 372.Google Scholar