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The Second Solution of Mathieu's Differential Equation

Published online by Cambridge University Press:  24 October 2008

S. Goldstein
S. Goldstein
Affiliation:
St John's College, Isaac Newton Student
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Extract

The Mathieu functions of period π and 2π have recently been constructed by the help of analysis similar to that developed by Laplace, Kelvin, Darwin and Hough to find the free tides symmetrical about the axis of a rotating globe. The purpose of this note is to show that a similar construction can be carried out for the second solution of the Mathieu equation, when one solution is periodic in π or 2π, by the help of analysis similar to that used for forced tides. The construction is effected in a form suitable for numerical computation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 24 , Issue 2 , April 1928 , pp. 223 - 230
Copyright
Copyright © Cambridge Philosophical Society 1928

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References

* Trans. Camb. Phil. Soc., Vol. XXIII, p. 303 (1927).Google ScholarSee also Ince, , Proc. Roy. Soc. Edin., Vol. XLVI, p. 20 and p. 316 (1926), and Vol. XLVII, p. 294 (1927).Google Scholar

† Lamb, , Hydrodynamics, fifth edition, p. 313.Google Scholar

‡ Proc. Edin. Math. Soc., Vol. XXXIII, p. 2 (1915);Google ScholarProc. Camb. Phil. Soc., Vol. XXIII, p. 47 (1926).Google Scholar

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* Trans. Camb. Phil. Soc., Vol. XXIII, p. 330.Google Scholar

* Trans. Camb. Phil. Soc., Vol. XXIII, p. 303.Google Scholar

* This point was overlooked in Trans. Camb. Phil. Soc., Vol. XXIII, p. 330, where F was taken as 1.Google Scholar