bigfloats of special functions (e.g. Bessel).. wasRe: integrate bessel_j errcatch?
Subject: bigfloats of special functions (e.g. Bessel).. wasRe: integrate bessel_j errcatch?
From: Raymond Toy
Date: Thu, 8 Dec 2011 11:05:44 -0800
On Thu, Dec 8, 2011 at 9:30 AM, Richard Fateman
<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