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: Richard Fateman
Date: Thu, 08 Dec 2011 11:59:10 -0800
On 12/8/2011 11:05 AM, Raymond Toy wrote:
> 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 just glanced at it and although I may be misunderstanding, my
impression is that
this paper is aimed at finding an acceptable absolute error, which does
not really do the
job -- you need acceptable relative error (precision, that is). How
hard is it
to evaluate those series accurately??
I suppose the same analysis techniques could be used though... yet the
approaches from
numerical analysts seem so different from this.
For example, evaluation of a Bessel function near a zero of that
function needs some
special work. One approach is to expand in a Taylor series about that
zero...