Let $R>0,$ $D_R=\{z\in \mathbb{C} / |z|<R\}$; I am trying to show that if $f$ holomorphic on $D_R$ and continue on $\bar D_R$, and $w$ is an arbitrary point in $D_R$, then $$f(w)=\frac{R^2}{\pi}\int_{D_R}\frac{f(z)}{(R^2-\bar{z}w)^{2}}d\lambda{(z)} \qquad \text{For all}\quad w\in D_R$$ Where $d\lambda{(z)} = \frac{i}{2}dz\wedge d\bar z = dxdy$ .
I already shown the fomula for $R=1$, so I tried to prove it for $R>0$ but I wasn't successful.
Hint: For $|z|\le 1,$ define $f_R(z) = f(Rz).$ Then $f_R$ is holomorphic on $D_1$ and continuous on $\overline {D_1}.$ Apply the $R=1$ formula and then make the change of variables $z=u/R,u\in D_R.$