ドッティ数
D = 1 − ( 1 − ( ∫ − ∞ ∞ 16 ( z − sinh  ( z ) ) 2 + 12 π 2 ( 4 ( z − sinh  ( z ) ) 2 + 3 π 2 ) 2 + 16 π 2 ( z − sinh  ( z ) ) 2 d z ) − 1 ) 2 {\displaystyle D={\sqrt {1-\left(1-\left(\int _{-\infty }^{\infty }{\frac {16(z-\sinh(z))^{2}+12\pi ^{2}}{\left(4(z-\sinh(z))^{2}+3\pi ^{2}\right)^{2}+16\pi ^{2}(z-\sinh(z))^{2}}}\,dz\right)^{-1}\right)^{2}}}} .
D = π 2 − 1 2 π ∫ 0 ∞ ln  ( 2 π cosh  ( x ) + π 2 x 2 + cosh 2  ( x ) + 1 ) d x {\displaystyle D={\frac {\pi }{2}}-{\frac {1}{2\pi }}\int _{0}^{\infty }\ln \left({\frac {2\pi \cosh(x)+\pi ^{2}}{x^{2}+\cosh ^{2}(x)}}+1\right)\,dx}