From: "Charles H. Giffen" Subject: Re: Bessel function algoritm Date: Tue, 06 Jul 1999 14:19:35 -0400 Newsgroups: sci.math To: normanfowler@my-deja.com normanfowler@my-deja.com wrote: > > Does anyone know of a good algorithm for > numerically calculating standard Bessel > functions? In particular, in BASIC or Visual > Basic? > > Any help would be appreciated. > > Sincerely, > > Norman Fowler > > Sent via Deja.com http://www.deja.com/ > Share what you know. Learn what you don't. One has the asymptotic expansion J[p](x) = (2/(\pi x))^{1/2}\cos( x - \pi/4 - p\pi/2 ) + r(x)/x^{3/2}, where r(x) is bounded as x --> infinity. This suggests using the series expansion of J[p](x) for |x| less than some constant and using the above asymptotic expansion for large |x| (how large the constant is will be determined by the accuracy desired in the computation of J[p](x) ). Also, for non-negative integers p, one has J[1](x) = -J[0]'(x) and J[p+1](x) = 2pJ{p](x)/x - J[p-1](x), so by computing first just J[0](x) and J[1](x), one can compute J[p](x) recursively. --Chuck Giffen