Follow-up Comment #1, bug #54998 (group gsl): The Moshier reference is in https://www.moshier.net/methprog.pdf . The problem within the GSL implementation is that F_2 is returned with the wrong sign. This is triggered by a=-0.25 being negative, d_2=0 such that GAMMA(a+d_2) in the denominator of the prefactor of F_2 is negative. Because the implementation actually implements the Gamma(c)*(1-x)^d_1 /GAMMA(a+d2)/GAMMA(b+d2) by computing the logarithm of this, it actually computes the logarithm of an negative factor and gets the wrong branch. GSL returns is F_1+(-1)*F_2 (with |d|=1) so it returns 0.90031631-0.02027 but should have returned 0.90031+0.02027.
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