\[(1-z)^{-c+\mathrm{i}y}{{}_{2}F_{1}}\left({a+\mathrm{i}y,b+\mathrm{i}y\atop a+b%
};z\right)=\sum_{n=0}^{\infty}\frac{S_{n}\left(y^{2};a,b,c\right)}{{\left(a+b%
\right)_{n}}n!}z^{n},\]