[math-fun] I just found this and I should sleep on it before posting,

but just in case it's still mysterious in the "morning": What is this? QPolyGamma[0, 1/2, q] + QPolyGamma[0, 1/2 - (I π)/Log[q], q] == -Log[(1 - q)/(1 + q)] + QPolyGamma[0, 1/2, q^2] q-Euler's constants? In[1199]:= PolyGamma[0, 1/2] // FunctionExpand Out[1199]= -EulerGamma - Log[4] Empirically true in the 1st quadrant of the unit disk, and in the whole 4th quadrant. Does it generalize? Does q-digamma have a Jacobi imaginary transformation? zzzzzzzzzz.... --rwg