- #1
sit.think.solve
- 9
- 0
Suppose that
[tex]
\alpha_1,...,\alpha_n
[/tex]
are positive numbers. Show that
[tex]
\int_{1}^{\infty}...\int_{1}^{\infty}\frac{dx_1...dx_n}{{x_1}^{\alpha_1}+...+{x_n}^{\alpha_n}}<\infty
[/tex]
if
[tex]
\frac{1}{\alpha_1}+...+\frac{1}{\alpha_n}<1
[/tex]
[tex]
\alpha_1,...,\alpha_n
[/tex]
are positive numbers. Show that
[tex]
\int_{1}^{\infty}...\int_{1}^{\infty}\frac{dx_1...dx_n}{{x_1}^{\alpha_1}+...+{x_n}^{\alpha_n}}<\infty
[/tex]
if
[tex]
\frac{1}{\alpha_1}+...+\frac{1}{\alpha_n}<1
[/tex]