Date: Tue, 10 Jul 2012 09:50:45 -0700 From: Steve Kargl <sgk@troutmask.apl.washington.edu> To: Stephen Montgomery-Smith <stephen@missouri.edu> Cc: freebsd-current@freebsd.org Subject: Re: Use of C99 extra long double math functions after r236148 Message-ID: <20120710165045.GA94795@troutmask.apl.washington.edu> In-Reply-To: <4FFC5ADF.2010601@missouri.edu> References: <20120529045612.GB4445@server.rulingia.com> <20120708124047.GA44061@zim.MIT.EDU> <210816F0-7ED7-4481-ABFF-C94A700A3EA0@bsdimp.com> <4FF9DA46.2010502@missouri.edu> <20120708235848.GB53462@troutmask.apl.washington.edu> <4FFA25EA.5090705@missouri.edu> <20120709020107.GA53977@troutmask.apl.washington.edu> <4FFA52F8.2080700@missouri.edu> <20120709050238.GA54634@troutmask.apl.washington.edu> <4FFC5ADF.2010601@missouri.edu>
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On Tue, Jul 10, 2012 at 11:39:59AM -0500, Stephen Montgomery-Smith wrote: > On 07/09/2012 12:02 AM, Steve Kargl wrote: > > >Yep. Another example is the use of upward recurion to compute > >Bessel functions where the argument is larger than the order. > >The algorithm is known to be unstable. > > By upward recursion, do you mean equation (1) in > http://mathworld.wolfram.com/BesselFunction.html? Yes. > So what do people use. Maybe something like > http://en.wikipedia.org/wiki/Bessel_function#Asymptotic_forms (second > set of equations), but finding some asymptotics with a few extra terms > in them? They use downward recursion, which is known to be stable. NIST has revised Abramowitz and Stegun, and it is available on line. For Bessel function computations, look at http://dlmf.nist.gov/10.74 and more importantly example 1 under the following link http://dlmf.nist.gov/3.6#v -- Steve
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