\underset{n\to \infty }{\text{lim}}\underset{m\to \infty }{\text{lim}}2 \pi  r \sqrt{h^2+\frac{\pi ^4 n^2 r^2}{4 m^4}}

 x \left(\frac{(2 r) \sqrt{y^2} y}{y}+O\left(y^4\right)\right)+x^3 \left(-\frac{r \sqrt{y^2} y}{3 y}+O\left(y^4\right)\right)+O\left(x^4\right)