Conformal mapping onto a circular polygon with double simmetry

A conformal mapping of the unit disk $E=\{\xi\in\boldsymbol C\colon|\xi|<1\}$ onto a circular $2n$-gon, $n\in\boldsymbol N\setminus\{1\}$, with $n$-fold symmetry of rotation relatively to the point $w=0$ and with symmetry relatively to the straight $l=\left\{w\in\boldsymbol C\colon\operatorname{arg}w=\frac\pi n\right\}$ has been obtained in the integral form.