Kim, Taekyun Sums of powers of consecutive \(q\)-integers. (English) Zbl 1069.11009 Adv. Stud. Contemp. Math., Kyungshang 9, No. 1, 15-18 (2004). For any \(k\in\mathbb Z\), define the \(q\)-integer \([k]_q\) as \([k]_q=(q^k-1)/(q-1)\), where \(q\) is an indeterminate. The author computes a formula for the sum \(\sum_{j=0}^{k-1}q^{hj}[j]_q^n\), where \(k,h,n\in \mathbb Z\) and \(k,n>0\). The result is analogous to the classical formula for \(\sum_{j=0}^{k-1}j^n.\) Reviewer: Veikko Ennola (Turku) Cited in 18 Documents MSC: 11B68 Bernoulli and Euler numbers and polynomials 11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.) Keywords:\(q\)-integer; \(q\)-Bernoulli number; \(p\)-adic \(q\)-integral PDFBibTeX XMLCite \textit{T. Kim}, Adv. Stud. Contemp. Math., Kyungshang 9, No. 1, 15--18 (2004; Zbl 1069.11009) Full Text: arXiv