* high precision evaluation of special functions with free software
@ 2007-02-09 15:31 Brian Gough
2007-02-10 10:06 ` Axel Vogt
0 siblings, 1 reply; 3+ messages in thread
From: Brian Gough @ 2007-02-09 15:31 UTC (permalink / raw)
To: gsl-discuss
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.
^ permalink raw reply [flat|nested] 3+ messages in thread
* Re: high precision evaluation of special functions with free software
2007-02-09 15:31 high precision evaluation of special functions with free software Brian Gough
@ 2007-02-10 10:06 ` Axel Vogt
2007-02-12 9:09 ` Brian Gough
0 siblings, 1 reply; 3+ messages in thread
From: Axel Vogt @ 2007-02-10 10:06 UTC (permalink / raw)
To: Brian Gough; +Cc: gsl-discuss
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 ).
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2007-02-09 15:31 high precision evaluation of special functions with free software Brian Gough
2007-02-10 10:06 ` Axel Vogt
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