@article{2b085a8287854ca2beae95a2d4c5b1c9, title = "On the Asymptotics of the Jacobi Function and Its Zeros", abstract = " Explicit and realistic error bounds are constructed for a one-term and a two-term asymptotic approximation of the Jacobi function $\varphi _\mu ^{(\alpha ,\beta )} (t)$ as $\mu \to \infty $, uniformly for $t \in (0,\infty )$. A similar result is obtained for the zeros $t_{\mu ,k} $ of this function as $\mu \to \infty $, which holds uniformly with respect to unbounded k. Exponentially decaying error bounds are also given for asymptotic approximations of $\varphi _\mu ^{(\alpha ,\beta )} (t)$ as $t \to \infty $ and of $t_{\mu ,k} $ as $k \to \infty $, which are uniform for $\mu \geqq \delta > 0$. ", author = "WONG, {Sue Cheun Roderick} and Wang, {Q. Q.}", year = "1992", doi = "10.1137/0523090", language = "English", volume = "23", pages = "1637--1649", journal = "SIAM Journal on Mathematical Analysis", issn = "0036-1410", publisher = "Society for Industrial and Applied Mathematics", number = "6", }