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On the Inversion of the Gauss Transformation, II

Published online by Cambridge University Press:  20 November 2018

P. G. Rooney
P. G. Rooney*
Affiliation:
University of Toronto
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In an earlier paper (5) we studied the inversion theory of the Gauss transformation defined by

(1.1). Operational methods indicated that and we showed that in certain circumstances this equation was true if exp (— D2) f(x) was interpreted as the sum of the series

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 613 - 616
Copyright
Copyright © Canadian Mathematical Society 1958 

Footnotes

This work was done while the author held a summer research associateship of the National Research Council of Canada.

References

1. Erdélyi et al., A, Tables of Integral Transforms I, (New York, 1954).Google Scholar
2. Hardy, G. H., Divergent Series (Oxford, 1949).Google Scholar
3. McShane, E. J., Integration (Princeton, 1944).Google Scholar
4. Pollard, Harry, Integral transforms, Duke Math. J., 13 (1946), 307–330.Google Scholar
5. Rooney, P. G., On the inversion of the Gauss transformation, Can. J. Math., 9 (1957), 459-465.Google Scholar
6. Titchmarsh, E. C., An Introduction to the Theory of Fourier Integrals (2nd ed.; Oxford, 1948).Google Scholar