structural:summarization, linguistic:paraphrasing, structural:reformatting
Wallis product

The Wallis infinite product for π {\displaystyle \pi }

π 2 = ∏ n = 1 ∞ 4 n 2 4 n 2 − 1 = ∏ n = 1 ∞ (2 n 2 n − 1 ⋅ 2 n 2 n + 1) = (2 1 ⋅ 2 3) ⋅ (4 3 ⋅ 4 5) ⋅ (6 5 ⋅ 6 7) ⋅ (8 7 ⋅ 8 9) ⋅ ⋯ {\displaystyle {\begin{aligned}{\frac {\pi }{2}}&=\prod _{n=1}^{\infty }{\frac {4n^{2}}{4n^{2}-1}}=\prod _{n=1}^{\infty }\left({\frac {2n}{2n-1}}\cdot {\frac {2n}{2n+1}}\right)\\&={\Big (}{\frac {2}{1}}\cdot {\frac {2}{3}}{\Big)}\cdot {\Big (}{\frac {4}{3}}\cdot {\frac {4}{5}}{\Big)}\cdot {\Big (}{\frac {6}{5}}\cdot {\frac {6}{7}}{\Big)}\cdot {\Big (}{\frac {8}{7}}\cdot {\frac {8}{9}}{\Big)}\cdot \;\cdots \end{aligned}}}

may be derived using integration by parts.