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29 Lamé FunctionsLamé Polynomials

§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 0zK, 0zK, when nk and nk assume large real values. The approximating functions are exponential, trigonometric, and parabolic cylinder functions.