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.

Can this integral be done analytically? \begin{eqnarray} & & \int\limits^1_0 d\eta \: \eta^{ 1 - 2 \epsilon}\, ( 1 - \eta)^{1/2 - \epsilon} \, \left( 1 + 2 \sqrt{z} - \left( 1 - 2 \sqrt{z} \right) \eta \right)^{1/2 - \epsilon} \left(z + \left( 1 - 2 \sqrt{z} \right) \eta \right)^{-2 + \epsilon} \\ && \qquad {} \times {}_2 F_1 \left(1, \epsilon ; 2 - \epsilon; \frac{ z }{ z + \left( 1 - 2 \sqrt{z} \right) \eta }\right) \end{eqnarray} with $0 < z < \frac{1}{4}$.

share|improve this question
2  
kld, since you are a new user, here are a few things about the site you should know: 1. To get the best possible answers, it is helpful if you say where the problem originated, 2. You will get a better response, if you indicate, what you have already tried to answer the question yourself. 3. If this is homework, please add the [homework] tag; people will still help, so don't worry. and finally: Welcome to math.SE! –  draks ... Jul 19 '12 at 11:55
1  
@draks, somehow the hypergeometric function being there makes me doubt that this is homework... –  J. M. Jul 19 '12 at 11:56
    
@J.M. , depends. Didn't you do any homework at university? Sure you did... –  draks ... Jul 19 '12 at 12:03
    
@draks, well, all the things I know about special functions, I never learned at the university... :) –  J. M. Jul 19 '12 at 12:05
    
I believe this kind of integrals comes from statistical and physical applications. –  Mhenni Benghorbal Jul 19 '12 at 13:25
add comment

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.