\[\mathit{H\!\ell}\left(4,\alpha\beta;\alpha,\beta,\tfrac{1}{2},\tfrac{2}{3}(%
\alpha+\beta);z\right)={{}_{2}F_{1}}\left(\tfrac{1}{3}\alpha,\tfrac{1}{3}\beta%
;\tfrac{1}{2};1-(1-z)^{2}(1-\tfrac{1}{4}z)\right),\]