# On the Asymptotics of the Jacobi Function and Its Zeros

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

## Author(s)

• Sue Cheun Roderick WONG
• Q. Q. Wang

## Detail(s)

Original language English 1637-1649 SIAM Journal on Mathematical Analysis 23 6 Published - 1992 Yes

## 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 $\mu \geqq \delta > 0$.

## Citation Format(s)

[ RIS ] [ BibTeX ]

On the Asymptotics of the Jacobi Function and Its Zeros. / WONG, Sue Cheun Roderick; Wang, Q. Q. .

In: SIAM Journal on Mathematical Analysis, Vol. 23, No. 6, 1992, p. 1637-1649.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review