A Note on Stirling Series
نویسندگان
چکیده
We study sums S = S(d, n, k) = ∑ j≥1 [ d] jk( j )j! with d ∈ N = {1, 2, . . . } and n, k ∈ N0 = {0, 1, 2, . . . } and relate them to (finite) multiple zeta functions. As a byproduct of our results we obtain asymptotic expansions of ζ(d + 1) −H n as n tends to infinity. Furthermore, we relate sums S to Nielsen’s polylogarithm.
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