q-analogues of the sums of powers of consecutive integers

@inproceedings{Kim2005qanaloguesOT,
  title={q-analogues of the sums of powers of consecutive integers},
  author={Taekyun Kim},
  year={2005}
}
Let n, k be the positive integers (k > 1), and let Sn,q(k) be the sums of the n-th powers of positive q-integers up to k − 1: Sn,q(k) = ∑k−1 l=0 ql. Following an idea due to J. Bernoulli, we explore a formula for Sn,q(k). 

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