*Quad>* Hey all. Does anyone have any ideas on computing Bessel functions to high precision (over the complex plane)? Googling gives [1] and [2]. Sorry, [1] is behind a paywall. I am wondering if one of you has a secret magical sum or product that just magically works well for high precision computation. If not, maybe we can develop some strategies! Thanks, Robert Smith [1] dl.acm.org/citation.cfm?id=1466254 [2] web.cs.dal.ca/~jborwein/bessel.pdf *------ You're of course welcome to my Macsyma code. At the time, I used (a tiny fraction of) Watson's Treatise, but now there's dlmf*.nist.gov/10 . My only novelty was using matrix products to do the series--merely a small constant speedup. I may not even have gotten around to handling the asymptotics. Do you suspect Mathematica knows something we don't? --rwg