수학2 케일리 해밀턴 정리와 관련 정리들 2021. 6. 3. 1 + 1/4 + 1/9 + 1/16 + 1/25 + ... = ? https://math.stackexchange.com/questions/229631/show-that-int-0-1-times-0-1-fracdx-dy1-xy-frac-pi26 Show that $\int_{[0,1]\times [0,1]}\frac{dx \, dy}{1-xy} = \frac{\pi^2}{6}$ $$ \int_{[0,1] \times [0,1]} \frac{dx \, dy}{1-xy}=\frac{\pi^2}{6}, $$ there is a hint for substitution given but I can't seem to get anywhere with it. $$ \begin{cases} x = \frac{u-v}{\sqrt{2}} \\ ... math.stackexchange.co.. 2021. 5. 23. 이전 1 다음
