Uniform asymptotic expansion of the Jacobi polynomials in a complex domain
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 2569-2586 |
| Journal / Publication | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| Volume | 460 |
| Issue number | 2049 |
| Publication status | Published - 8 Sept 2004 |
Link(s)
Abstract
An asymptotic formula is found that links the behaviour of the Jacobi polynomial Pn(α,β)(z) in the interval of orthogonality [-1,1] with that outside the interval. The two infinite series involved in this formula are shown to be exponentially improved asymptotic expansions. The method used in this paper can also be adopted in other cases of orthogonal polynomials such as Hermite and Laguerre. © 2004 The Royal Society.
Research Area(s)
- Complex domain, Exponential improvement, Jacobi polynomials, Uniform asymptotic expansion
Citation Format(s)
Uniform asymptotic expansion of the Jacobi polynomials in a complex domain. / Wong, R.; Zhao, Yu-Qiu.
In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 460, No. 2049, 08.09.2004, p. 2569-2586.
In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 460, No. 2049, 08.09.2004, p. 2569-2586.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
