乗法的不定和分
∏ x f ( x ) g ( x ) = ∏ x f ( x ) ∏ x g ( x ) , {\displaystyle \prod _{x}f(x)g(x)=\prod _{x}f(x)\prod _{x}g(x),}
∏ x f ( x ) a = ( ∏ x f ( x ) ) a , {\displaystyle \prod _{x}f(x)^{a}=\left(\prod _{x}f(x)\right)^{a},}
∏ x a f ( x ) = a ∑ x f ( x ) . {\displaystyle \prod _{x}a^{f(x)}=a^{\sum _{x}f(x)}.}
周期函数 f(x) の周期 T に対して
∏ x f ( T x ) = C f ( T x ) x − 1 {\displaystyle \prod _{x}f(Tx)=Cf(Tx)^{x-1}}
が成り立つ。