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Fractional Integration and Dual Integral Equations

Published online by Cambridge University Press:  20 November 2018

A. Erdélyi  and
I. N. Sneddon
A. Erdélyi
Affiliation:
California Institute of Technology
I. N. Sneddon
Affiliation:
The University Glasgow
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In the analysis of mixed boundary value problems by the use of Hankel transforms we often encounter pairs of dual integral equations which can be written in the symmetrical form

(1.1)

Equations of this type seem to have been formulated first by Weber in his paper (1) in which he derives (by inspection) the solution for the case in which α — β = ½, v = 0, F ≡ 1, G ≡ 0.

The first direct solution of a pair of equations of this type was given by Beltrami (2) for the same values of α— β and v with G(p) ≡ 0 but with F(ρ) arbitrary.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 14 , 1962 , pp. 685 - 693
Copyright
Copyright © Canadian Mathematical Society 1962

References

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