Sinc関数
∫ 0 ∞ sinc 2  ( x ) d x = 1 2 , ∫ − ∞ ∞ sinc 2  ( x ) d x = 1 ( sinc 2  ( x ) = { sinc  ( x ) } 2 ) {\displaystyle \int _{0}^{\infty }\operatorname {sinc} ^{2}(x)\,dx={\frac {1}{2}},\quad \int _{-\infty }^{\infty }\operatorname {sinc} ^{2}(x)\,dx=1\quad \left(\operatorname {sinc} ^{2}(x)=\{\operatorname {sinc} (x)\}^{2}\right)}
∫ 0 ∞ | sinc  ( x ) | d x = ∞ , ∫ − ∞ ∞ | sinc  ( x ) | d x = ∞ {\displaystyle \int _{0}^{\infty }|\operatorname {sinc} (x)|\,dx=\infty ,\quad \int _{-\infty }^{\infty }|\operatorname {sinc} (x)|\,dx=\infty }