\[\Phi^{(\alpha,\beta)}_{\lambda}(t)=(2\cosh t)^{\mathrm{i}\lambda-\alpha-\beta-%
1}F\left({\tfrac{1}{2}(\alpha+\beta+1-\mathrm{i}\lambda),\tfrac{1}{2}(\alpha-%
\beta+1-\mathrm{i}\lambda)\atop 1-\mathrm{i}\lambda};{\operatorname{sech}}^{2}%
t\right).\]