On the Width of the Instability Intervals of the Mathieu Equation

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1984 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Mathematical Analysis, volume 15, pages 105-107 (issn: 0036-1410, eissn: 1095-7154,

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Authors: Hochstadt, Harry;

doi: 10.1137/0515005

On the Width of the Instability Intervals of the Mathieu Equation

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Abstract

It is shown that the width of the m-th instability interval of the Mathieu equation is given asymptotically by \[ (8h^{2m}/4^ m[(m- 1)!]^ 2)[1+O(h^ 4/m^ 2)]. \] The method of proof is based on a continued fraction technique using three term recursion formulas.

Keywords

Mathieu equation, width, instability interval, Ordinary differential operators, recursion formulas, continued fraction technique, Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)

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