Take the 2-minute tour ×
Mathematica Stack Exchange is a question and answer site for users of Mathematica. It's 100% free, no registration required.

I want to compute the following sum over primes: $$\sum\limits_{p \text{ prime}}\sum\limits_{k=1}^\infty(\log(p^k))\left(\frac{1}{2p^k} - \Phi[-1,1,p^k]\right),$$ where $\Phi[z,s,a]$ is the Hurwitz-Lerch transcendent. Can I compute it using Mathematica? Here is the code I used

Sum[log((Prime[n])^k) ( Prime[n])^(-k)/2-HurwitzLerchPhi[-1,1,Prime[n]^k]), 
                                        {k, 1, Infinity}, {n, 1, Infinity}]
share|improve this question
Duplicate: Double sum over primes –  rm -rf Nov 9 '13 at 15:58
You asked a similar question previously and ignored requests made to you to post the code you had developed. Again you post no code. Why should we help you? This is not a free coding service. –  m_goldberg Nov 9 '13 at 16:07
I suggest to leave open this question. Perhaps it might have a symbolic solution. Nonetheless the linked post provides possible ways for an approximate sum. –  Artes Nov 9 '13 at 21:50
@Artes I saw your comment just now... do you suggest reopening it? –  rm -rf Nov 9 '13 at 22:11
@rm-rf I'd rather be more careful with this question. Probably this sum can be only approximated numerically, but I'm not sure. Perhaps someone might find an exact sum. I guess we would leave it open for one or two days. –  Artes Nov 9 '13 at 22:20
show 2 more comments

migrated from scicomp.stackexchange.com Nov 9 '13 at 15:41

This question came from our site for scientists using computers to solve scientific problems.

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.