Some rapidly converging series for <IMG ALIGN=MIDDLE HEIGHT=32 WIDTH=80>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

Some rapidly converging series for

Authors:	H M Srivastava

Institution:	Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada~~V8W~3P4

Abstract:	For a natural number , the author derives several families of series representations for the Riemann Zeta function $\zeta (2n+1)$ . Each of these series representing $\zeta (2n+1)$ converges remarkably rapidly with its general term having the order estimate: $\begin{equation}O(k^{-2n-1}\cdot m^{-2k})\qquad (k\to \infty ;\quad m=2,3,4,6).\end{equation}$ Relevant connections of the results presented here with many other known series representations for $\zeta (2n+1)$ are also pointed out.

Keywords:	Zeta functions binomial theorem Pochhammer symbol functional equation harmonic numbers l'H\^{o}pital's rule Bernoulli numbers Euler polynomials Euler's formula

	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