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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
G. H. Hardy
Affiliation:
Trinity College, Cambridge
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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
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 36 , Issue 1 , January 1940 , pp. 1 - 8
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
(2)Bateman, H. “The polynomial F n(x)”. Annals of math. 35 (1934), 767–75.CrossRefGoogle Scholar
(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