par Hoffman, Michael M.E.;Kuba, Markus;Levy, Moti;Louchard, Guy
Référence The Ramanujan journal
Publication Publié, 2020
Article révisé par les pairs
Résumé : We obtain an asymptotic series ∑j=0∞Ijnj for the integral ∫01[xn+(1-x)n]1ndx as n→ ∞, and compute Ij in terms of alternating (or “colored”) multiple zeta values. We also show that Ij is a rational polynomial in the ordinary zeta values, and give explicit formulas for j≤ 12. As a by-product, we obtain precise results about the convergence of norms of random variables and their moments. We study Zn= ‖ (U, 1 - U) ‖ n as n tends to infinity and we also discuss Wn=‖(U1,U2,⋯,Ur)‖n for standard uniformly distributed random variables.