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1: 28 Mathieu Functions and Hill’s Equation

Chapter 28 Mathieu Functions and Hill’s Equation

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2: 28.29 Definitions and Basic Properties

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§28.29(i) Hill’s Equation

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§28.29(ii) Floquet’s Theorem and the Characteristic Exponent

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3: 28.32 Mathematical Applications

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§28.32(ii) Paraboloidal Coordinates

… ►is separated in this system, each of the separated equations can be reduced to the Whittaker–Hill equation (28.31.1), in which $A,B$ are separation constants. …

4: Simon Ruijsenaars

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28 Mathieu Functions and Hill’s Equation

5: Bibliography U

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Theory of the Whittaker-Hill equation. Proc. Roy. Soc. Edinburgh Sect. A 69, pp. 28–44.

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External Links:

MathReview (R. K. Rathy), ZentralBlatt

Referenced by:

§28.31(i), §28.31(ii), §28.32(ii).

Encodings:

BibTeX

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6: 28.31 Equations of Whittaker–Hill and Ince

§28.31 Equations of Whittaker–Hill and Ince

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§28.31(i) Whittaker–Hill Equation

►Hill’s equation with three terms …and constant values of $A,B,k$, and $c$, is called the Equation of Whittaker–Hill. … ►

§28.31(ii) Equation of Ince; Ince Polynomials

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7: 28.30 Expansions in Series of Eigenfunctions

§28.30 Expansions in Series of Eigenfunctions

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§28.30(i) Real Variable

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8: Gerhard Wolf

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28 Mathieu Functions and Hill’s Equation

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9: 28.34 Methods of Computation

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Asymptotic approximations by zeros of orthogonal polynomials of increasing degree. See Volkmer (2008). This method also applies to eigenvalues of the Whittaker–Hill equation (§28.31(i)) and eigenvalues of Lamé functions (§29.3(i)).

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10: 29.7 Asymptotic Expansions

… ►Weinstein and Keller (1985) give asymptotics for solutions of Hill’s equation (§28.29(i)) that are applicable to the Lamé equation.