Even rational Parseval integral

Applying the Parseval identity to the repeated exponential convolution gives

\int_{- \infty}^{\infty} \frac{d k}{( 1 + k ^{2} ) ^{n + 1}} = \frac{π ( 2 n )!}{2 ^{2 n} ( n ! ) ^{2}} = \frac{π}{4 ^{n}} (n 2 n) .

 Ancestors (6)