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[Helpgsl] Need help with negative arguments to gsl_sf_ellint_Kcomp, com
From: 
Jerry 
Subject: 
[Helpgsl] Need help with negative arguments to gsl_sf_ellint_Kcomp, complete elliptic integral of the first kind 
Date: 
Fri, 24 Apr 2015 02:55:52 0700 
Hi list,
I'm having trouble understanding how to use gsl_sf_ellint_Kcomp, the complete
elliptic integral of the first kind, K(k).
First, gsl_sf_ellint_Kcomp has a domain limited to 1 < k < +1 and raises an
error for arguments outside that range.
Second, gsl_sf_ellint_Kcomp defines a function with even symmetry around k = 0.

The corresponding Octave, Mathematica, and I presume Matlab functions are all
nonsymmetric and they all decay towards zero as the argument tends to from +1
to infinity. (Mathematica also returns a real result for arguments > 1.)
Octave and Mathematica both reference Abramowitz & Stegun without
qualification, whereas the GSL reference says that "Note that Abramowitz &
Stegun define this function in terms of the parameter m = k^2."
For arguments between 0 and 1, taking the square root before passing to
gsl_sf_ellint_Kcomp returns a result consistent with the other references
herein (Octave, Mathematica). However, I don't know how to get results for
arguments less than zero that are also consistent with those references.
Abramowitz & Stegun provides a bunch of ways of handling various kinds of
arguments but I can't find one that is suitable.
For what it's worth, this function arises in the probability density function
of the sum of two random sine variables. For unitamplitude sine RVs, the
argument to gsl_sf_ellint_Kcomp is always between 0 and 1 so to proceed with
programming that problem I don't really need to have the question herein
answered, but I would like to know how to handle it in the future should it
arise.
Thanks for any help.
Jerry
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