Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I came across these integrals and I'm trying to rewrite them in terms of Dilogarithms: $\mathrm{Li}_2(z):=-\int_0^z \frac{\mathrm{d}s}{s}\log(1-s)$. Can anyone suggest how to contunue? If there is a good change of variables to be done for instance.

$$\int _0^1\mathrm{d}a\int _0^{1-a}\ln \left((a-1+b)^2-4 y a b\right)\mathrm{d}b\\[7mm]+4 (1-y)\int_0^1 \mathrm{d}a\int _0^{1-a}\frac{(a-1+b)^2}{(a-1+b)^2-4 y a b}\mathrm{d}b$$

I see a pattern in $(a+b-1)^2$ but can't think of a good change of variables to get the second integral in a simple form.

The first integration (that with respect to $b$ say) can be done straightforward but the second integration cannot all be done in analytic form so I'm trying to write it in the form of dilogarithms. Any suggestions how to continue?

share|cite|improve this question
Please do not use titles consisting only of math expressions; these are discouraged for technical reasons -- see meta. – arjafi May 31 '13 at 7:08
OK the problem was that the characters ran out. But I see your point. – Mauchy May 31 '13 at 7:38

Your Answer


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

Browse other questions tagged or ask your own question.