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Date: Tue, 10 Jul 2012 09:50:45 -0700
From: Steve Kargl <sgk@troutmask.apl.washington.edu>
To: Stephen Montgomery-Smith <stephen@missouri.edu>
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Cc: freebsd-current@freebsd.org
Subject: Re: Use of C99 extra long double math functions after r236148
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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