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Generating Functions for Hermite Functions

Published online by Cambridge University Press:  20 November 2018

Louis Weisner
Louis Weisner*
Affiliation:
University of New Brunswick
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Hermite's function Hn(x) is denned for all complex values of x and n by

where F (α; γ; x) is Kummer's function with the customary indices omitted. It satisfies the differential equation

1.1

of which

is a second solution. Every solution of (1.1) is an entire function.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 11 , 1959 , pp. 141 - 147
Copyright
Copyright © Canadian Mathematical Society 1959

References

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3. Mehler, F. G., Ueber die Entwicklung einer Funktion von beliebig vielen Variablen nach Laplaceschen Functionen hôherer Ordnung, J. Reine Angew. Math., 66 (1866), 161–76.Google Scholar
4. Truesdell, C., An essay toward a unified theory of special functions, Ann. Math. Studies, no. 18 (Princeton, 1948).Google Scholar
5. Weisner, L., Group-theoretic origin of certain generating functions, Pacific J. Math. 5 (1955), 1033-9.Google Scholar