Some alternating sums of multiple zeta values of height one
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.124957
Abstract: Abstract In this paper, we construct several double sequences arising from double integrals which can be interpreted as alternating sums of multiple zeta values. The aim of the article is based on generating functions and… read more here.
Keywords: zeta; sums multiple; zeta values; multiple zeta ... See more keywords
Factors of Sums and Alternating Sums of Products of $q$-binomial Coefficients and Powers of $q$-integers
Sign Up to like & getrecommendations! Published in 2019 at "Taiwanese Journal of Mathematics"
DOI: 10.11650/tjm/180601
Abstract: We prove that, for all positive integers $n_1, \ldots, n_m$, $n_{m+1}=n_1$, and non-negative integers $j$ and $r$ with $j\leqslant m$, the following two expressions \begin{align*} &\frac{1}{[n_1+n_m+1]}{n_1+n_{m}\brack n_1}^{-1}\sum_{k=0}^{n_1} q^{j(k^2+k)-(2r+1)k}[2k+1]^{2r+1}\prod_{i=1}^m {n_i+n_{i+1}+1\brack n_i-k},\\[5pt] &\frac{1}{[n_1+n_m+1]}{n_1+n_{m}\brack n_1}^{-1}\sum_{k=0}^{n_1}(-1)^k q^{{k\choose 2}+j(k^2+k)-2rk}[2k+1]^{2r+1}\prod_{i=1}^m {n_i+n_{i+1}+1\brack… read more here.
Keywords: binomial coefficients; sums alternating; powers integers; alternating sums ... See more keywords