# A q-Analogue of Faulhaber's Formula for Sums of Powers

@article{Guo2005AQO,
title={A q-Analogue of Faulhaber's Formula for Sums of Powers},
author={Victor J. W. Guo and Jiang Zeng},
journal={Electron. J. Comb.},
year={2005},
volume={11}
}
• Published 2005
• Mathematics, Computer Science
• Electron. J. Comb.
• Let $$S_{m,n}(q):=\sum_{k=1}^{n}\frac{1-q^{2k}}{1-q^2} \left(\frac{1-q^k}{1-q}\right)^{m-1}q^{\frac{m+1}{2}(n-k)}.$$ Generalizing the formulas of Warnaar and Schlosser, we prove that there exist polynomials $P_{m,k}(q)\in{\Bbb Z}[q]$ such that $$S_{2m+1,n}(q) =\sum_{k=0}^{m}(-1)^kP_{m,k}(q) \frac{(1-q^n)^{m+1-k}(1-q^{n+1})^{m+1-k}q^{kn}} {(1-q^2)(1-q)^{2m-3k}\prod_{i=0}^{k}(1-q^{m+1-i})},$$ and solve a problem raised by Schlosser. We also show that there is a similar formula for the… CONTINUE READING

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