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.
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- $\begingroup$ It is a related question I could not find the value of this sum $\endgroup$Surya– Surya2013-10-14 12:55:55 +00:00Commented 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– Artes2013-10-14 12:58:19 +00:00Commented 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– Michael E22013-10-14 21:40:08 +00:00Commented Oct 14, 2013 at 21:40
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