论文标题
Stieltjes常数的高精度数值计算。简单而快速的算法
The High Precision Numerical Calculation of Stieltjes Constants. Simple and Fast Algorithm
论文作者
论文摘要
我们提出了一种简单但有效的方法，用于以很高的精度计算stieltjes常数，高达约80000个显着数字。该方法基于一位作者在1997年\ Cite {Maslanka 1}提出的Riemann Zeta函数的超几何样膨胀。该方法中的关键成分是在同样间隔的真实参数中计算得出的Riemann Zeta函数的一系列高精度数值序列，即$ζ（1+ \ varepsilon），ζ（1+2 \ 2 \ 2 \ varepsilon），ζ（1+3 \ varepsilon），... （在主要文本中描述了$ \ varepsilon $的实际选择。）可以使用Pari/GP程序轻易获得Zeta的值，这特别适合于此。
We present a simple but efficient method of calculating Stieltjes constants at a very high level of precision, up to about 80000 significant digits. This method is based on the hypergeometric-like expansion for the Riemann zeta function presented by one of the authors in 1997 \cite{Maslanka 1}. The crucial ingredient in this method is a sequence of high-precision numerical values of the Riemann zeta function computed in equally spaced real arguments, i.e. $ζ(1+\varepsilon),ζ(1+2\varepsilon),ζ(1+3\varepsilon),...$ where $\varepsilon$ is some real parameter. (Practical choice of $\varepsilon$ is described in the main text.) Such values of zeta may be readily obtained using the PARI/GP program, which is especially suitable for this.
