On the irrationality of a certain multivariate <IMG > series期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

On the irrationality of a certain multivariate series

Authors:	Peter B Borwein Ping Zhou

Institution:	Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6 ; Department of Mathematics, Statistics & Computer Science, St. Francis Xavier University, Antigonish, Nova Scotia, Canada B2G 2W5

Abstract:	We prove that for integers $q>1,m\geq 1$ and positive rationals $r_1,r_2,\cdots ,r_m\neq q^j,j=1,2,\cdots ,$ the series $\begin{displaymath}\sum_{j=1}^\infty \frac{q^{-j}}{\left( 1-q^{-j}r_1\right) \left( 1-q^{-j}r_2\right) \cdots \left( 1-q^{-j}r_m\right) } \end{displaymath}$ is irrational. Furthermore, if all the positive rationals $r_1,r_2,\cdots ,r_m$ are less than then the series $\begin{displaymath}\sum_{j_1,\cdots ,j_m=0}^\infty \frac{r_1^{j_1}\cdots r_m^{j_m}}{ q^{j_1+\cdots +j_m+1}-1} \end{displaymath}$ is also irrational.

Keywords:

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文