Jonathan Borwein (Jon) receives funding from the Australian Research Council. Often described as “the most beautiful formula in mathematics”, Euler seems never to have actually written it down – ...

An asymptotic expansion is obtained, as $\lambda \rightarrow +\infty$, for the integral $$I(\lambda) = \int^{\pi/2}_0 J^2_\nu(\lambda \cos \theta)d\theta,$$ where $J ...