総乗
ウォリス積
∏ n = 1 ∞ ( 2 n ) 2 ( 2 n − 1 ) ( 2 n + 1 ) = π 2 {\displaystyle \prod _{n=1}^{\infty }{\frac {(2n)^{2}}{(2n-1)(2n+1)}}={\frac {\pi }{2}}}
オイラー乗積
ζ ( s ) = ∏ p : prime 1 1 − p − s {\displaystyle \zeta (s)=\prod _{p:{\text{prime}}}{\frac {1}{1-p^{-s}}}}
ガンマ関数
1 Γ ( z ) := z e γ z ∏ m = 1 ∞ ( 1 + z m ) e − z / m , γ := lim n → ∞ ( ∑ k = 1 n 1 k − log  n ) {\displaystyle {\frac {1}{\Gamma (z)}}:=ze^{{\gamma }z}\prod _{m=1}^{\infty }\left(1+{\frac {z}{m}}\right)e^{-z/m},\quad \gamma :=\lim _{n\to \infty }\left(\sum _{k=1}^{n}{\frac {1}{k}}-\log {n}\right)}