Question Number 162701 by mnjuly1970 last updated on 31/Dec/21
Answered by phanphuoc last updated on 31/Dec/21
$$\phi\left({a},{b}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{a}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{{b}} {dx}=\mathrm{1}/\mathrm{2}{B}\left(\left({a}+\mathrm{1}\right)/\mathrm{2},\left(\mathrm{2}{b}+\mathrm{1}\right)/\mathrm{2}\right) \\ $$$$\partial^{\mathrm{2}} \left(\phi\right)/\partial\left({a}^{\mathrm{2}} \right)\partial\left({b}^{\mathrm{2}} \right)=….. \\ $$$${a}=−\mathrm{2},{b}=\mathrm{1} \\ $$