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VI.—Generating Functions of Certain Continuous Orthogonal Systems

Published online by Cambridge University Press:  14 February 2012

A. Erdélyi
A. Erdélyi
Affiliation:
Mathematical Institute, University of Edinburgh
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Summary

10. Generating functions and bilinear generating functions (of the type of Mehler's celebrated formula) are known to be of great importance in the formal theory of orthogonal sequences. The present paper contains analogous formulae for a number of continuous orthogonal systems as well as “mixed” systems (which have a point spectrum as well as a continuous one). Four systems of the hypergeometric type have been selected as examples which are thought to be of some importance because of their presenting themselves in certain problems of Mathematical Physics.

My thanks are due to the Carnegie Trust for the Universities of Scotland for grants towards the printing of this paper and my paper in Proceedings, vol. lx, no. 26, 1940.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 61 , Issue 1 , 1941 , pp. 61 - 70
Copyright
Copyright © Royal Society of Edinburgh 1941

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References

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