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On certain expansions of the solutions of Mathieu'S differential equation

Published online by Cambridge University Press:  24 October 2008

A. Erdélyi
A. Erdélyi
Affiliation:
Mathematical InstituteThe UniversityEdinburgh 1 Communicated by E. T. Whittaker
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Extract

1. There are several known types of expansions of Mathieu functions, i.e. mod 2π periodic solutions of Mathieu's equation ((9), chap. 19),

The simplest expansion is the Fourier series

Almost equally well known are Heine's expansion ((4), p. 414; see also (5) and (6))

and

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 38 , Issue 1 , January 1942 , pp. 28 - 33
Copyright
Copyright © Cambridge Philosophical Society 1942

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References

REFERENCES

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