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.

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

For notational convenience, let $f(t) = a^2 + 2 a b \cdot \cos(t) + b^2$, where $a,b$ are both positive real constants and $t$ will be the integrand of the integral, which is supposed to be carried out from $t=0$ to $t=2 \pi$. I want to find an expression (or approximations) for \begin{align} \int\limits_0^{2\pi} \frac{\exp(-c(24m^2 - 24m \sqrt{f(t)} + 7 f(t) - 4 a b \cdot \cos(t)))}{(m^2\cdot f(t))^{1/4}} dt \end{align} where $c,m$ are again positive real constants.

My first attempt was to use Mathematica, but without any result. Are there maybe any tricks how to approximate the above integral? Any comments or suggestions are most welcome! Thanks in Advance.

share|cite|improve this question

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.