An Asymptotic Series for an Integral

Michael E. Hoffman, Markus Kuba, Moti Levy +1

We obtain 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 compute $I_j$ in terms of alternating…