This account is temporarily suspended for rule violations. The suspension period ends on Dec 25 at 9:15.
1 reputation
52652
bio website sites.google.com/site/drmhennibenghorbal/Home
location
age
visits member for 2 years, 3 months
seen 12 hours ago

Some deleted answers! Some of them are accepted and the other are correct. I just would like to keep them at hand.

(1)- (2)- (3)- (4)- (5).

Is there a closed form for $\sum_{j=1}^{n} j^2\log{j}$?

$$ -\zeta' \left( -2 \right) +\zeta_1' \left( -2,n+1 \right). $$

A more general case

$$ \sum_{k=1}^{n} j^{s}\ln(j)^{m}= \lim_{\alpha \to s } \zeta^{(m)}_{\alpha}( - \alpha ) + \zeta^{(m)}_{\alpha} \left( -\alpha,n+1 \right). $$


14
Sep 19 '12 at 7:48
11
Aug 30 '13 at 5:51
11
Apr 3 '13 at 21:30
10
Aug 14 '12 at 23:41
8
Feb 26 '13 at 14:57