Trong các ứng dụng với hàm đặc biệt, các tích vô hạn sau có ích:

sin ⁡ x = x ∏ n = 1 ∞ ( 1 − x 2 π 2 n 2 ) {\displaystyle \sin x=x\prod _{n=1}^{\infty }\left(1-{\frac {x^{2}}{\pi ^{2}n^{2}}}\right)} sinh ⁡ x = x ∏ n = 1 ∞ ( 1 + x 2 π 2 n 2 ) {\displaystyle \sinh x=x\prod _{n=1}^{\infty }\left(1+{\frac {x^{2}}{\pi ^{2}n^{2}}}\right)} cos ⁡ x = ∏ n = 1 ∞ ( 1 − x 2 π 2 ( n − 1 2 ) 2 ) {\displaystyle \cos x=\prod _{n=1}^{\infty }\left(1-{\frac {x^{2}}{\pi ^{2}(n-{\frac {1}{2}})^{2}}}\right)} cosh ⁡ x = ∏ n = 1 ∞ ( 1 + x 2 π 2 ( n − 1 2 ) 2 ) {\displaystyle \cosh x=\prod _{n=1}^{\infty }\left(1+{\frac {x^{2}}{\pi ^{2}(n-{\frac {1}{2}})^{2}}}\right)} sin ⁡ x x = ∏ n = 1 ∞ cos ⁡ ( x 2 n ) {\displaystyle {\frac {\sin x}{x}}=\prod _{n=1}^{\infty }\cos \left({\frac {x}{2^{n}}}\right)}