论文标题
关于Apery常数方法的注释
Notes On An Approach To Apery's Constant
论文作者
论文摘要
莱昂哈德·欧拉（Leonhard Euler）在1734年解决的巴塞尔问题要求解决自然数字正方形的倒数的总和，即无限序列的总和：\ begin {equation} \sum_{i=1}^{\infty}\frac{1}{n^2}=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\ldots\notag \end{equation} The same question is posed regarding the summation of the自然数量的立方体的倒数，$ζ（3）$。结果常数被称为apery的常数。 YouTube频道3BlueBrown制作了一个标题为“为什么在这里Pi？为什么它是平方的视频？对巴塞尔问题的几何答案”。该视频展示了约翰·瓦斯兰德的作品。方程可以扩展到$ζ（n）$，但是几何参数丢失了。我们尝试以$ζ（n）$来探索这些方程式。
The Basel problem, solved by Leonhard Euler in 1734, asks to resolve $ζ(2)$, the sum of the reciprocals of the squares of the natural numbers, i.e. the sum of the infinite series: \begin{equation} \sum_{i=1}^{\infty}\frac{1}{n^2}=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\ldots\notag \end{equation} The same question is posed regarding the summation of the reciprocals of the cubes of the natural numbers, $ζ(3)$. The resulting constant is known as Apery's constant. A YouTube channel, 3BlueBrown, produced a video entitled, "Why is pi here? And why is it squared? A geometric answer to the Basel problem". The video presents the work of John Wästlund. The equations can be extended to $ζ(n)$, but the geometric argument is lost. We try to explore these equations for $ζ(n)$.
