Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How to calculate the following integral: for positive constants $a_1, \cdots, a_{n+1}, $ and $i>0$ $$ \int_{S^n\bigcap\{u_m\geq 0,\ m=1,\cdots, n+1\}}\left(\sum_{m=1}^{n+1} \frac{u_m}{a_m}\right)^{-i}du, $$ where $u=(u_1, \cdots, u_{n+1})\in S^n,$ the unit sphere.

Thanks a lot!

share|improve this question
    
Have you tried evaluating it for some small $n$? Do you think the method can be generalized to any $n$? –  Pedro Tamaroff Jun 15 '12 at 2:30
    
Try it out of some values, may is not enough to be sure. –  Pedro Tamaroff Jun 15 '12 at 2:56
    
The evaluating process may be the same for any $n.$ In fact, I need it may less than $$C(\frac{a_1\cdots a_{n+1}}{a_2\cdots a_{n+1}})^i$$ if $a_1\leq\cdots\leq a_{n+1}.$ –  mathpdE Jun 15 '12 at 2:58

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.