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.
Improving an old idea of Hermite, we associate to each natural number k a modified zeta function of order k. The evaluation of the values of these functions F k at positive integers reveals a wide class of identities linking Cauchy numbers, harmonic numbers and zeta values.
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