§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 $0\leq\realpart{z}\leq\!\mathop{K\/}\nolimits\!$, $0\leq\imagpart{z}\leq\!\mathop{{K^{\prime}}\/}\nolimits\!$, when $nk$ and $nk^{\prime}$ assume large real values. The approximating functions are exponential, trigonometric, and parabolic cylinder functions.