160309

sinc function の積の積分(2)

書き方を変えてみたが、規則性がわからなかった。

∫(0,∞)sinc(x)dx = 1 / 2 × π

∫(0,∞)sinc(x)sinc(x / 2)dx = 1 / 2 × π

∫(0,∞)sinc(x)sinc(x / 2)sinc(x / 3)dx = 1 / 2 × π

∫(0,∞)sinc(x)sinc(x / 2)…sinc(x / 4)dx = (1 / 2 - 1 / 3456) × π

∫(0,∞)sinc(x)sinc(x / 2)…sinc(x / 5)dx = (1 / 2 - 83521 / 41472000) × π

∫(0,∞)sinc(x)sinc(x / 2)…sinc(x / 6)dx = (1 / 2 - 14331857 / 4147200000) × π

∫(0,∞)sinc(x)sinc(x / 2)…sinc(x / 7)dx = (1 / 2 - 231768210132197 / 50185433088000000) × π