TY - JOUR
T1 - On the Asymptotics of the Jacobi Function and Its Zeros
AU - WONG, Sue Cheun Roderick
AU - Wang, Q. Q.
PY - 1992
Y1 - 1992
N2 -
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 $\mu \geqq \delta > 0$.
AB -
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 $\mu \geqq \delta > 0$.
U2 - 10.1137/0523090
DO - 10.1137/0523090
M3 - 21_Publication in refereed journal
VL - 23
SP - 1637
EP - 1649
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 6
ER -