On Louchard's Asymptotic Series

Michael E. Hoffman

Recently G. Louchard obtained an asymptotic series ${\sum }_{j=0}^{\infty }\frac{I_j}{n^j}$ for the integral ${\int }_0^1[x^n+(1-x{)}^n{]}^{\frac{1}{n}}dx$ as $n\to \infty$, and computed $I_j$ for $…