Follow-up Comment #2, bug #54998 (group gsl): The patch would be to replace the calls to gsl_sf_lngamma_e() by calls to gsl_sf_lngamma_sgn_e() and to multiply F1 and F2 by the product of the signs of the Gamma-prefactors. More important would be to flag gsl_sf_lngamma_e() with an error if the sign is negative. Currently the sign is actually computed in gsl_sf_lngamma_e() but this effect is hidden in the gsl_sf_result.
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