[Help-gsl] Re: Incomplete elliptic integral (Legendre) (quasi-)periodicity issue

[Lionel B]

On Fri, 09 Feb 2007 20:49:17 +0000, Brian Gough wrote:

> At Fri, 27 Oct 2006 12:43:05 +0100,
> Lionel Barnett wrote:
>> It appears that the function gsl_sf_ellint_E(phi,m) is periodic with
>> period 2\pi. However, E(\phi|m), even under the definition at:
>> 
>> http://www.gnu.org/software/gsl/manual/html_node/Definition-of-Legendre-Forms.html#Definition-of-Legendre-Forms
>> 
>> is actually *quasi*-periodic, satisfying the relation:
>> 
>> E(\phi+n\pi,m) = 2n E(m) + E(\phi,m)
>> 
>> Now I can use this relationship to calculate the correct value of
>> E(\phi,m) for larger \phi ... except for \pi/2 < \phi < \pi
>> 
> 
> Just to let you know this has now been fixed in CVS for the next
> release (http://sources.redhat.com/gsl/devel.html) - the values should
> be correct for all values of phi now.

Much appreciated (and apologies for not having got round to submitting
that bug report).

Regards,

-- 
Lionel B