Uniform asymptotic expansion of Jν (νa) via a difference equation
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
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Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 147-193 |
| Journal / Publication | Numerische Mathematik |
| Volume | 91 |
| Issue number | 1 |
| Publication status | Published - Mar 2002 |
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Abstract
There are two ways of deriving the asymptotic expansion of Jν(νa), as ν → ∞, which holds uniformly for a ≥ 0. One way starts with the Bessel equation and makes use of the turning point theory for second-order differential equations, and the other is based on a contour integral representation and applies the theory of two coalescing saddle points. In this paper, we shall derive the same result by using the three term recurrence relation Jν+1 (x) + Jν-1(x) = (2ν/x) Jν(x). Our approach will lead to a satisfactory development of a turning point theory for second-order linear difference equations.
Citation Format(s)
Uniform asymptotic expansion of Jν (νa) via a difference equation. / Wang, Z.; Wong, R.
In: Numerische Mathematik, Vol. 91, No. 1, 03.2002, p. 147-193.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
