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Notes on special systems of orthogonal Functions (III): A System of orthogonal polynomials

Published online by Cambridge University Press:  24 October 2008

G. H. Hardy
Affiliation:
Trinity College, Cambridge

Extract

Generalities. Suppose that

is real and L2(0, ∞), that

is its Mellin transform, and that

Then K(1)(x) generates a “Watson transformation”, with a “Fourier theorem”

valid for every F(x) of L2(0, ∞).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1940

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References

REFERENCES

(1)Bateman, H.Some properties of a certain set of polynomials”. Tóhoku math. J. 37 (1933), 23–8.Google Scholar
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(3)Hardy, G. H.Notes on some points in the integral calculus (46–47)”. Messenger of math. 46 (1917), 175–82, and 47 (1918), 81–8.Google Scholar
(4)Titchmarsh, E. C.Theory of Fourier integrals (Oxford, 1937).Google Scholar