# Expressing a function by generalizations of the Zeta function

I was doing some calculations and I've come to the point where I have to study the function defined (formally) as:

$$f(x)=\sum_{n=0}^\infty \frac 1{(n+1)^x(n+2)}$$

And I thought I may express it as some generalization of the famous Zeta function (Multiple Zeta, Multiple Hurwitz, Shintani, ecc.) mainly because there are tons of results on the subject and this would probably speed up my calculations, however I didn't went so far as I'm not too familiar with zeta functions.

• For integer values of $x$, it seems that it should be a linear combination fo zeta functions. – Claude Leibovici Sep 21 '17 at 11:59
• @ClaudeLeibovici yeah I did some calculations, however I hope to get to a general as possible result – Renato Faraone Sep 21 '17 at 12:00