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On the Equation of the Parabolic Cylinder Functions

Published online by Cambridge University Press:  20 January 2009

Arch Milne
Arch Milne
Affiliation:
Research Student, Edinburgh University, Mathematical Laboratory.
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Hermite, in 1864 (Comptes Rendus, vol. 58) introduced into analysis the polynomials defined by the relation

where n is a positive integer. He showed that they satisfied the differential equation

that they were orthogonal functions, and that an arbitrary function f(x) could be expanded in the form

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , February 1913 , pp. 2 - 14
Copyright
Copyright © Edinburgh Mathematical Society 1913