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A Note on Stirling Series
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Published/Copyright:
September 9, 2010
Abstract
We study sums 
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 
as n tends to infinity. Furthermore, we relate sums S to Nielsen's polylogarithm.
Received: 2009-04-08
Revised: 2010-03-30
Accepted: 2010-04-08
Published Online: 2010-09-09
Published in Print: 2010-September
© de Gruyter 2010
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Articles in the same Issue
- Two New Van Der Waerden Numbers: w(2; 3, 17) and w(2; 3, 18)
- Distance Graphs from p-adic Norms
- A Note on Stirling Series
- On the Number of Certain Relatively Prime Subsets of {1, 2, . . . , n}
- Powers of Sierpiński Numbers Base b
- Subsets of ℤ with Simultaneous Orderings
- Alternative Proofs on the 2-adic Order of Stirling Numbers of the Second Kind
- On Relatively Prime Sets Counting Functions
- Congruences for Overpartition k-tuples
Keywords for this article
Stirling numbers of the first kind;
multiple zeta values;
harmonic numbers
Articles in the same Issue
- Two New Van Der Waerden Numbers: w(2; 3, 17) and w(2; 3, 18)
- Distance Graphs from p-adic Norms
- A Note on Stirling Series
- On the Number of Certain Relatively Prime Subsets of {1, 2, . . . , n}
- Powers of Sierpiński Numbers Base b
- Subsets of ℤ with Simultaneous Orderings
- Alternative Proofs on the 2-adic Order of Stirling Numbers of the Second Kind
- On Relatively Prime Sets Counting Functions
- Congruences for Overpartition k-tuples
