bigfloats of special functions (e.g. Bessel).. wasRe: integrate bessel_j errcatch?

On 12/8/2011 11:05 AM, Raymond Toy wrote:
>
>
> On Thu, Dec 8, 2011 at 9:30 AM, Richard Fateman 
> <fateman at eecs.berkeley.edu <mailto:fateman at eecs.berkeley.edu>> wrote:
>
>     On 11/9/2011 12:44 PM, Barton Willis wrote:
>
>         In addition to being slow, only the 2F1 hypergeometric
>         function analytically continues to outside the convergence disk.
>
>         --Barton
>
>
>     I have been looking around at the literature on "unrestricted
>     algorithms" for elementary and special functions,
>     esp. work by Richard Brent.
>
>     These are algorithms appropriate for bigfloats in that instead of
>     compute sin(x), or bessel_j(0,x),
>     for a given x,   take another parameter n, where n is the number
>     of bits of precision required.
>
>
> Do you have a link?  I looked sometime ago for some algorithms for 
> bessel functions and only found one using Hadamard series 
> (http://www.sciencedirect.com/science/article/pii/S0377042708001799) 
> and some variations thereof.  Never got them to converge but I only 
> spent a short time on them.  The algorithms weren't difficult, but I 
> was not smart enough to get them to converge.
>
> Ray

I started with
http://arxiv.org/PS_cache/arxiv/pdf/1004/1004.3621v1.pdf by Richard Brent

which seems to be dated 2010, and has lots of references.

RJF