# Generalization of summation of k^a

Hello everybody,

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

## Answers and Replies

fzero
Homework Helper
Gold Member
Gib Z
Homework Helper
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.

Thank you for your useful helps. :)