The Arakawa-Kaneko Zeta Function Marc-Antoine Coppo and Bernard Candelpergher

We present a very natural generalization of the Arakawa-Kaneko zeta function introduced ten years ago by T. Arakawa and M. Kaneko. We give in particular a new expression of the special values of this function at integral points in terms of modified Bell polynomial. By rewriting Ohno’s sum formula, we are in a position to deduce a new class of relations between Euler sums and the values of zeta. Mathematical Subject Classification (2000) : Primary 11M41, 11M35 ; secondary 40-02, 40-03.