TY - JOUR
T1 - Uniform asymptotic expansion of Jν (νa) via a difference equation
AU - Wang, Z.
AU - Wong, R.
PY - 2002/3
Y1 - 2002/3
N2 - 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.
AB - 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.
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U2 - 10.1007/s002110100316
DO - 10.1007/s002110100316
M3 - RGC 21 - Publication in refereed journal
VL - 91
SP - 147
EP - 193
JO - Numerische Mathematik
JF - Numerische Mathematik
SN - 0029-599X
IS - 1
ER -