ボールウェイン積分
∫ 0 ∞ sin  ( x ) x sin  ( x / 3 ) x / 3 ⋯ sin  ( x / 13 ) x / 13 d x = π / 2 {\displaystyle \int _{0}^{\infty }{\frac {\sin(x)}{x}}{\frac {\sin(x/3)}{x/3}}\cdots {\frac {\sin(x/13)}{x/13}}\,dx=\pi /2}
ところが、次のステップではこのパターンが崩れてしまう。
∫ 0 ∞ sin  ( x ) x sin  ( x / 3 ) x / 3 ⋯ sin  ( x / 15 ) x / 15 d x = 467807924713440738696537864469 935615849440640907310521750000 π = π 2 − 6879714958723010531 935615849440640907310521750000 π ≃ π 2 − 2.31 × 10 − 11 {\displaystyle {\begin{aligned}\int _{0}^{\infty }{\frac {\sin(x)}{x}}{\frac {\sin(x/3)}{x/3}}\cdots {\frac {\sin(x/15)}{x/15}}\,dx&={\frac {467807924713440738696537864469}{935615849440640907310521750000}}\pi \\&={\frac {\pi }{2}}-{\frac {6879714958723010531}{935615849440640907310521750000}}\pi \\&\simeq {\frac {\pi }{2}}-2.