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1: 28 Mathieu Functions and Hill’s Equation
Chapter 28 Mathieu Functions and Hill’s Equation
2: 28.29 Definitions and Basic Properties
§28.29(i) Hill’s Equation
§28.29(ii) Floquet’s Theorem and the Characteristic Exponent
3: 28.32 Mathematical Applications
§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
5: Bibliography U
  • K. M. Urwin and F. M. Arscott (1970) Theory of the Whittaker-Hill equation. Proc. Roy. Soc. Edinburgh Sect. A 69, pp. 28–44.
  • 6: 28.30 Expansions in Series of Eigenfunctions
    §28.30 Expansions in Series of Eigenfunctions
    §28.30(i) Real Variable
    7: Gerhard Wolf
    8: 28.31 Equations of Whittaker–Hill and Ince
    §28.31 Equations of Whittaker–Hill and Ince
    §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
    9: 28.34 Methods of Computation
  • (f)

    Asymptotic approximations by zeros of orthogonal polynomials of increasing degree. See Volkmer (2008). This method also applies to eigenvalues of the Whittaker–Hill equation28.31(i)) and eigenvalues of Lamé functions (§29.3(i)).

  • 10: 29.7 Asymptotic Expansions
    Weinstein and Keller (1985) give asymptotics for solutions of Hill’s equation28.29(i)) that are applicable to the Lamé equation.