@article{d0469eed0e66413b96afc2ce99d7ef1f, title = "Uniform asymptotic expansion of Jν (νa) via a difference equation", 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.", author = "Z. Wang and R. Wong", year = "2002", month = mar, doi = "10.1007/s002110100316", language = "English", volume = "91", pages = "147--193", journal = "Numerische Mathematik", issn = "0029-599X", publisher = "Springer", number = "1", }