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

Consider the integral: $$f(s)=\frac{1}{2\pi i}\int_{\tau-i\infty}^{\tau+i\infty}\frac{\zeta(z)}{z}\left[\psi\left(\frac{z}{s} \right ) +\frac{s}{2z}-\log\left(\frac{z}{s} \right )\right ]dz\;\;\;\;(\tau<0)$$ $\zeta(\cdot)$ being the Riemann zeta function, and $\psi\left(\cdot\right)$ being the Digamma function. We wish for an explicit evaluation of integral, possibly with a proof that $f(s)$ has an analytic continuation to the whole complex plane, except for a branch cut along the $s$ imaginary axis.

share|cite|improve this question
    
i don't see how this is a Mellin-type integral ! – Mohammad Al Jamal Aug 3 '13 at 21:09
    
Sorry , that was a stupid suggest – Zaid Alyafeai Aug 3 '13 at 21:12

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.