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Determinants connected with the Periodic Solutions of Mathieu's Equations

Published online by Cambridge University Press:  20 January 2009

A. G. Burgess
A. G. Burgess
Affiliation:
Research Student, Edinburgh University Mathematical Laboratory
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Various solutions of Mathieu's equation, or the equation of the elliptic cylinder functions

have recently been discussed in an elegant series of papers in these Proceedings. These papers have dealt with the periodic and quasi-periodic solutions, but the present paper merely considers determinants which give the infinite series of relations between a and q, so that the solutions are purely periodic, i.e. the solutions denoted by Professor Whittaker

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 33 , February 1914 , pp. 122 - 138
Copyright
Copyright © Edinburgh Mathematical Society 1914

References

* Liouville's Journal, sér 2, t. xiii., pp. 137–203.Google Scholar

† Proceedings of Edinburgh Mathematical Society, Vols. XXXII. and XXXIII. (Part 1.)Google Scholar

‡ Proceedings of the Mathematical Congress, 1912, Vol. I.Google Scholar

§ Hill, : Acta Mathematica, Vol. VIII., pp. 1–36, 1886.Google Scholar

* This remark applies to all the determinants derived.

† Cf. Young, : Proceedings of Edinburgh Mathematical Society, Vol. XXXIIGoogle Scholar. Ince, Lindsay: Proceedings of Edinburgh Mathematical Society, Vol. XXXIII. (Part 1.)Google Scholar