総乗
三角関数の無限乗積展開
sin  π z = π z ∏ n = 1 ∞ ( 1 − z 2 n 2 ) {\displaystyle \sin \pi z=\pi z\prod _{n=1}^{\infty }\left(1-{\frac {z^{2}}{n^{2}}}\right)}
cos  π z = ∏ n = 1 ∞ { 1 − z 2 ( n − 1 2 ) 2 } {\displaystyle \cos \pi z=\prod _{n=1}^{\infty }\left\{1-{\frac {z^{2}}{(n-{\frac {1}{2}})^{2}}}\right\}}
sinh  π z = π z ∏ n = 1 ∞ ( 1 + z 2 n 2 ) {\displaystyle \sinh \pi z=\pi z\prod _{n=1}^{\infty }\left(1+{\frac {z^{2}}{n^{2}}}\right)}
cosh  π z = ∏ n = 1 ∞ { 1 + z 2 ( n − 1 2 ) 2 } {\displaystyle \cosh \pi z=\prod _{n=1}^{\infty }\left\{1+{\frac {z^{2}}{(n-{\frac {1}{2}})^{2}}}\right\}}