Generalization of summation of k^a

[coki2000]

Hello everybody,

Are there any generalization of this summation $$\sum_{k=1}^{n}k^{a}$$ for a>3? Thanks for your responses.

 

[fzero]

Check equ (12) on http://mathworld.wolfram.com/PowerSum.html This doesn't look like much of a simplification, but it is a sum of only a+1 terms, instead of the original n, which is presumably much larger.

 

[Gib Z]

Faulhabers Formula: http://en.wikipedia.org/wiki/Faulhaber's_formula

We can derive expressions for many series with the Euler-Maclaruin formula. Applied to this, it leads to Faulhaber's formula. It can be applied to non-integer a as well.

 

[coki2000]

Thank you for your useful helps. :)