Question Number 182082 by SEKRET last updated on 04/Dec/22
$$\:\:\:\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\underset{\boldsymbol{\mathrm{r}}=\mathrm{0}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\left(\mathrm{1}\right)^{\boldsymbol{\mathrm{r}}} \:\centerdot\frac{\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{r}}} \boldsymbol{\mathrm{y}}^{\mathrm{2022}\left(\boldsymbol{\mathrm{n}}+\mathrm{2}\right)} }{\left(\boldsymbol{\mathrm{n}}−\boldsymbol{\mathrm{r}}\right)!\left(\boldsymbol{\mathrm{r}}!\right)^{\mathrm{2}} \left(\mathrm{2022}\boldsymbol{\mathrm{y}}^{\mathrm{2022}} +\mathrm{2023}\right)^{\mathrm{2}} }\boldsymbol{\mathrm{dxdy}} \\ $$$$ \\ $$$$ \\ $$