Sums of powers of consecutive q-integers

By Taekyun Kim. 2005

62 citations recorded by the source corpus.

. Let n, k be the positive integers ( k > 1) , and let S n,q ( k ) be the sums of the n -th powers of positive q -integers up to k − 1: S n,q ( k ) = P 1 l =0 q l [ l ] nq , where [ l ] q = q l − 1 q − 1 . Following an idea due to J. Bernoulli, we explore a formula for S n,q ( k ) as follows: where β i,q are the q -Bernoulli numbers.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1a1582548b01a7ede9f4fb8fbb5971150029d199

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

A note on p-adic q-Euler measure (2007, unknown): “n=0 En t n! , see [1], [2], [3], [4], [5], [6].”
$q$-Bernoulli Numbers and Polynomials Associated with Multiple $q$-Zeta Functions and Basic $L$-series (2005, background): “, 1) = β (r) n (w : q), where β n (w : q) are the q-Bernoulli polynomials of order r (see[18]), which reduces to the ordinary Bernoulli polynomials of higher order B (r) n (w) if q = 1 (see for detail [21], [23], [24]) Kim[22] defined the analytic continuation of multiple zeta functions ( the EulerB”