Three-Step and Four-Step Random Walk Integrals

This is a preprint by Jonathan M. Borwein, Armin Straub and James Wan (submitted).

Abstract

We investigate the moments of 3-step and 4-step uniform random walk in the plane. In particular, we further analyse a formula conjectured in BNSW expressing 4-step moments in terms of 3-step moments. Diverse related results including hypergeometric and elliptic closed forms for W₄(± 1) are given and two new conjectures are recorded.

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