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Generalisations of some Integrals Involving Bessel Functions and E-Functions

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. In § 3 a generalisation of the formula [MacRobert, Phil. Mag., Ser. 7, XXXI, p. 258]

where αp+1 = ½m + ½n, αp+2 = ½m - ½n, R(m ± n) > 0, and x is real and positive, will be established. In the course of the proof Hardy's formula [Mess, of Maths., LVI, (1927), p. 190],

where R(b)>0, will be required. This was originally proved by an application of Mellin's Inversion Formula. An alternative proof is given in § 2, and some related formulae are deduced.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 1 , Issue 2 , July 1952 , pp. 72 - 75
Copyright
Copyright © Glasgow Mathematical Journal Trust 1952