标题： 新迭代公式的应用用于计算$π$和具有$2$根的嵌套根式 显示英文标题

标题： Application of a new iterative formula for computing $π$ and nested radicals with roots of $2$

摘要： 在本工作中，我们得到一个迭代公式，可用于计算$\pi$的位数和类型为$c_n/\sqrt{2 - c_{n - 1}}$的嵌套根，其中 $c_0 = 0$和$c_n = \sqrt{2 + c_{n - 1}}$。 我们还展示了如何借助此迭代公式生成和近似$\pi$的两术语马钦类似公式。 给出了一些带有 Mathematica 代码的示例。 显示英文摘要

摘要： In this work, we obtain an iterative formula that can be used for computing digits of $\pi$ and nested radicals of kind $c_n/\sqrt{2 - c_{n - 1}}$, where $c_0 = 0$ and $c_n = \sqrt{2 + c_{n - 1}}$. We also show how with help of this iterative formula the two-term Machin-like formulas for $\pi$ can be generated and approximated. Some examples with Mathematica codes are presented.