Home » Uncategorized » A Gudermannian integral

A Gudermannian integral

Let n \in \mathbb{N}. Prove that

    \[\int_{0}^{\infty} \int_{0}^{\infty} \frac{\mathrm{gd}^n \left ( xy \right )}{\cosh xy} \sin y \, \mathrm{d} \left ( x, y \right ) = \frac{1}{n+1} \cdot \left ( \frac{\pi}{2} \right )^{n+2}\]

where \mathrm{gd} is the Gudermannian function.

Solution

Read more

1 Comment

Leave a comment

Donate to Tolaso Network