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 13:19:24 -0800
On 12/8/2011 12:58 PM, Raymond Toy wrote:
>
> 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
>
>
Sin, cos, are handled by (very accurate) range reduction, so a series
only has to be good for
something like 0<x<pi/8 or so.
exp and log can be dealt with by 'doubling' eg exp(x) = (exp(x/2))^2
recursively.
Bessel functions have nice identities, but not as nice as those.