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Two inequalities for parabolic cylinder functions

Published online by Cambridge University Press:  24 October 2008

F. W. J. Olver
F. W. J. Olver
Affiliation:
The National Physical Laboratory Teddington
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Extract

In this paper upper bounds are established for the principal solution of the differential equation

and its derivative, for unrestricted values of the complex variable t and the complex parameter μ. The results may have little interest in their own right, but they are of great value in developing the asymptotic theory of linear second-order differential equations in a domain containing two turning points. Equation (1·1) is the simplest example of a differential equation of this type.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 4 , October 1961 , pp. 811 - 822
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

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