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

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Author(s)

  • Sue Cheun Roderick WONG
  • Q. Q. Wang

Detail(s)

Original languageEnglish
Pages (from-to)1637-1649
Journal / PublicationSIAM Journal on Mathematical Analysis
Volume23
Issue number6
Publication statusPublished - 1992
Externally publishedYes

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)

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