Can anyone tell me the value of the sum $$\sum_{p\in \mathcal{P}}\sum_{n=1}^{\infty}\frac{\log (p^n)}{2}\left[\,p^{-n}-\psi\left(\frac{p^n+2}{2}\right)+\psi\left(\frac{p^n+1}{2}\right)\right].$$ $\psi(z)$ is the digamma function. The sum is over primes using Mathematica.

  • $\begingroup$ It is a related question I could not find the value of this sum $\endgroup$
    – Surya
    Oct 14, 2013 at 12:55
  • 1
    $\begingroup$ Read the answers to the linked question to get an idea how you could approximate the value. $\endgroup$
    – Artes
    Oct 14, 2013 at 12:58
  • 2
    $\begingroup$ Would you please post the code you used to try to find the sum? $\endgroup$
    – Michael E2
    Oct 14, 2013 at 21:40


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