Closed form for $\sum_{n=2}^\infty \frac{1}{n^2\log n}$

sequences-and-series riemann-zeta integration closed-form

The closed form means an expression containing only elementary functions. For your case no such a form exists. For more informations read these links:

http://www.frm.utn.edu.ar/analisisdsys/MATERIAL/Funcion_Gamma.pdf

http://en.wikipedia.org/wiki/Hölder%27s_theorem

http://en.wikipedia.org/wiki/Gamma_function#19th-20th_centuries:_characterizing_the_gamma_function

http://divizio.perso.math.cnrs.fr/PREPRINTS/16-JourneeAnnuelleSMF/difftransc.pdf

http://www.tandfonline.com/doi/abs/10.1080/17476930903394788?journalCode=gcov20

Some background are needed for your understanding and good luck with these referrences.

Related

Looking for an approach to mathematical notation wherein the universe is divided into disjoint worlds.
Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?
Does this random variable have a density?
Problem on EU commission
What is $0^{i}$?
Does $\sum_n |\sin n|^{cn^2}$ converge?
Integrate $\int_0^1 \frac{\ln(1+x^a)}{1+x}\, dx$
A generalization of the product of harmonic numbers to non-integer arguments
A "relative" of the exponential function
Irrationality of $\sqrt{15}$
Equilateral polygon in a plane
Formal Schemes Mittag-Leffler