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A Generalization of an Inversion Formula for the Gauss Transformation

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 [3] we considered an inversion formula for the Gauss transformation G defined by

1.1

We noted there that formally G is inverted by,

1.2

and we showed that if e-D2 is interpreted via the power series for the exponential function, that is if

1.3

then under certain conditions on φ,

1.4

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 6 , Issue 1 , January 1963 , pp. 45 - 53
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Erdélyi, A. et al., Higher Transcendental Functions II (New York, 1953).Google Scholar
2. Hirschman, I.I. and Widder, D. V., The Convolution Transform, (Princeton, 1955).Google Scholar
3. Rooney, P.G., On the inversion of the Gauss transformation, Can. J. Math., 9, (1957), 459-464.Google Scholar
4. Szego, G., Orthogonal Polynomials, (New York, 1959).Google Scholar
5. Zygmund, A., Trigonometric Series I and II, (Cambridge, 1959).Google Scholar