Follow-up Comment #2, bug #39056 (group gsl): Possibly related: the gsl_sf_hyperg_2F1_e function treats the case x=1 as a singularity, producing NaN in some instances, despite a fix that was introduced in 2008-01-09. The results are correct for x in the neighborhood (ie to the left) of 1. These are for specfunc/test_hyperg.c:
TEST_SF(s, gsl_sf_hyperg_2F1_e, (5, -0.5, 5, 0.9999999, &r),
3.1622776593361366e-04 , TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_hyperg_2F1_e, (1, -0.5, 1, 0.9999999, &r),
3.1622776593361366e-04 , TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_hyperg_2F1_e, (-5.0/2.0, -0.5, -3.0/2.0, 0.9999999, &r),
5.2704625519675739e-11 , TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_hyperg_2F1_e, (-5.0/2.0, -0.5, -5.0/2.0, 0.9999999, &r),
3.1622776593361366e-04 , TEST_TOL0, GSL_SUCCESS);
/* the following test cases fail
TEST_SF(s, gsl_sf_hyperg_2F1_e, (5, -0.5, 5, 1, &r), 0 , TEST_TOL0,
GSL_SUCCESS);
TEST_SF(s, gsl_sf_hyperg_2F1_e, (1, -0.5, 1, 1, &r), 0 , TEST_TOL0,
GSL_SUCCESS);
TEST_SF(s, gsl_sf_hyperg_2F1_e, (-5.0/2.0, -0.5, -3.0/2.0, 1, &r), 0 ,
TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_hyperg_2F1_e, (-5.0/2.0, -0.5, -5.0/2.0, 1, &r), 0 ,
TEST_TOL0, GSL_SUCCESS); */
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