PaXContinuedDiLog corresponds to
ContinuedDiLog in Package-X.
(*Just to load Package-X*)
PaXEvaluate[A0[1]];PaXContinuedDiLog uses X`ContinuedDiLog for
numerical evaluations
PaXContinuedDiLog[{3.2, 1.0}, {1.1, 1.0}]-1.7089
X`ContinuedDiLog[{3.2, 1.0}, {1.1, 1.0}]-1.7089
The same goes for derivatives and series expansions
D[PaXContinuedDiLog[{x, xInf}, {y, yInf}], x]-\frac{y (-\log (x+i \;\text{xInf}\epsilon )-\log (y+i \;\text{yInf}\epsilon ))}{1-x y}
Series[PaXContinuedDiLog[{x, xInf}, {y, yInf}], {x, 1, 2}]\mathcal{L}_2(1+i \;\text{xInf}\epsilon ,y+i \;\text{yInf}\epsilon )-\frac{(x-1) y \log (y+i \;\text{yInf}\epsilon )}{y-1}+\frac{(x-1)^2 \left(y^2 \log (y+i \;\text{yInf}\epsilon )-y^2+y\right)}{2 (y-1)^2}+O\left((x-1)^3\right)