JacobiQ corner case

[MikaelSlevinsky]

By Theorem 4.61.2 in Szegő's Orthogonal Polynomials, my edition, it turns out that the hypergeometric series ₂F₁ representation of Q_0^{(\alpha,\beta)} degenerates to ₁F₀ when alpha+beta+1=0, and this perfectly cancels with the powers to become constant. There is an alternative linearly independent solution to Jacobi's differential equation (à la Frobenius' method), and this issue reports that it has not been implemented yet.

The linearly independent solution is given in terms of a partial derivative with respect to beta, so perhaps this calls for an implementation by dual numbers, similar to the logkernel integrals.

This case is really a corner case, since alpha = beta = -1/2 is special anyway, and it appears to me that most exotic solutions are sought from (alpha,beta) in [-1/2,1/2]^2.