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gsl_sf_gegenpoly_n returning unexpected values

From: Jackson Vanover
Subject: gsl_sf_gegenpoly_n returning unexpected values
Date: Wed, 4 Mar 2020 09:49:20 -0800

Using version 2.6 of GSL from ftp://ftp.gnu.org/gnu/gsl/gsl-2.6.tar.gz

OS is Ubuntu 18.04.2 LTS

Hardware is a Dell workstation with a 3.60 GHz Intel i7-4790 and 32 GB
of RAM

Compiler is gcc 7.4.0 with the -w option

When the second argument is 0, mpmath and scipy's implementations of
the gegenbauer polynomial agree that the output should be uniformly 0,
but gsl_sf_gegenpoly_n consistently returns nonzero values. This
happens regardless of the value of the first argument, though in
particular when the first argument is 1 and the second is 0, the
function returns twice the third argument...

#include <gsl/gsl_sf.h>
#include <stdio.h>
#include <gsl/gsl_math.h>
#include <float.h>

int main (void){
        double out;
        out = gsl_sf_gegenpoly_n(1, 0, 5);

        printf("%.*f\n", DBL_DIG-1, out);
        printf("%.21e\n", out);
        return 0;

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