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 12:58:26 -0800
On Thu, Dec 8, 2011 at 11:59 AM, Richard Fateman
<fateman at eecs.berkeley.edu>wrote:
> 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<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??
>
Unfortunately, this isn't the paper I was actually using. I don't have the
link handy right now, but it was based on this idea.
>
>
> 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...
>
Yes, we could. But we don't do that for sin, so why do we need that for
Bessel?
Ray