Abstract
We present a new complex analytic proof of the two classical formulas evaluating the sum of powers of consecutive integers which involve Stirling or Eulerian numbers. Our method generalizes that recently obtained by the second and third author for the sum of squares.
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Notes
We could also let run the summation index from 0 to n for \(n\in \mathbb {N}\).
Note that the summation index j could as well begin with 1 instead of 0, because \(\left[ \begin{array}{c}m\\ 0\end{array}\right] =0\) for \(m\in \mathbb {N}^*\).
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Barman, K., Chakraborty, B. & Mortini, R. Two classical formulas for the sum of powers of consecutive integers via complex analysis. Complex Anal Synerg 10, 5 (2024). https://doi.org/10.1007/s40627-024-00131-3
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DOI: https://doi.org/10.1007/s40627-024-00131-3