Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-26T21:23:59.656Z Has data issue: false hasContentIssue false

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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