1—10 of 37 matching pages
§29.14 Orthogonality►Lamé polynomials are orthogonal in two ways. … ►
§29.12(i) Elliptic-Function Form… ►There are eight types of Lamé polynomials, defined as follows: … ►
§29.19 Physical Applications… ►
§29.19(ii) Lamé Polynomials…
§29.13(i) Eigenvalues for Lamé Polynomials… ► ►
§29.13(ii) Lamé Polynomials: Real Variable… ►
§29.13(iii) Lamé Polynomials: Complex Variable… ►
§29.20(ii) Lamé Polynomials… ►The corresponding eigenvectors yield the coefficients in the finite Fourier series for Lamé polynomials. … ►
§29.20(iii) Zeros►Zeros of Lamé polynomials can be computed by solving the system of equations (29.12.13) by employing Newton’s method; see §3.8(ii). …
§29.16 Asymptotic Expansions►Hargrave and Sleeman (1977) give asymptotic approximations for Lamé polynomials and their eigenvalues, including error bounds. The approximations for Lamé polynomials hold uniformly on the rectangle , , when and assume large real values. …
§29.22(ii) Lamé Polynomials… ►
LA3: Eigenvalues for Lamé polynomials.
LA4: Lamé polynomials.
10: 29.21 Tables
Ince (1940a) tabulates the eigenvalues , (with and interchanged) for , , and . Precision is 4D.
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.