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Re: high precision evaluation of special functions with free software
- From: Axel Vogt <mail at axelvogt dot de>
- To: Brian Gough <bjg at network-theory dot co dot uk>
- Cc: gsl-discuss at sourceware dot org
- Date: Sat, 10 Feb 2007 09:35:43 +0100
- Subject: Re: high precision evaluation of special functions with free software
- References: <87lkj72vrl.wl%bjg@network-theory.co.uk>
- Reply-to: mail at axelvogt dot de
Brian Gough wrote:
I needed to compute some high-precision (> double precision) test
cases for the Elliptic integrals and could not find anything to do it
- I usually use Pari-GP (GPL'ed) but it doesn't seem to have these.
If anyone has any suggestions for how to do this with free software,
I'd be glad to hear them.
Can't you use "intnum" in Pari? If there is a singularity inbetween
one splits the integration.
For example integrating F:= x -> 1/((1-x^2)^(1/2)*(1-k^2*x^2)^(1/2))
over the unit interval is EllipticK(k) and intnum(x = 0, 1/k, f(x))
+ intnum(x = 1/k, 1, f(x) gives it ( here for 0 < 1/k < 1 ).