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§29.19 Physical Applications►
§29.19(i) Lamé Functions►Simply-periodic Lamé functions ( noninteger) can be used to solve boundary-value problems for Laplace’s equation in elliptical cones. …Brack et al. (2001) shows that Lamé functions occur at bifurcations in chaotic Hamiltonian systems. Bronski et al. (2001) uses Lamé functions in the theory of Bose–Einstein condensates. …
Chapter 29 Lamé Functions…
§29.22(i) Lamé Functions… ►
LA1: Eigenvalues for Lamé functions.
LA2: Lamé functions.
§29.17(ii) Algebraic Lamé Functions►Algebraic Lamé functions are solutions of (29.2.1) when is half an odd integer. … ►
§29.17(iii) Lamé–Wangerin Functions►Lamé–Wangerin functions are solutions of (29.2.1) with the property that is bounded on the line segment from to . …
§29.20(i) Lamé Functions… ►The normalization of Lamé functions given in §29.3(v) can be carried out by quadrature (§3.5). … ►Subsequently, formulas typified by (29.6.4) can be applied to compute the coefficients of the Fourier expansions of the corresponding Lamé functions by backward recursion followed by application of formulas typified by (29.6.5) and (29.6.6) to achieve normalization; compare §3.6. … ►A third method is to approximate eigenvalues and Fourier coefficients of Lamé functions by eigenvalues and eigenvectors of finite matrices using the methods of §§3.2(vi) and 3.8(iv). …The approximations converge geometrically (§3.8(i)) to the eigenvalues and coefficients of Lamé functions as . …
7: 29.21 Tables
Arscott and Khabaza (1962) tabulates the coefficients of the polynomials in Table 29.12.1 (normalized so that the numerically largest coefficient is unity, i.e. monic polynomials), and the corresponding eigenvalues for , . Equations from §29.6 can be used to transform to the normalization adopted in this chapter. Precision is 6S.