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Generating Functions for Hermite Functions

Published online by Cambridge University Press:  20 November 2018

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
Copyright
Copyright © Canadian Mathematical Society 1959

References

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