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# Three-step and four-step random walk integrals

Three-step and four-step random walk integrals
Jonathan M. Borwein, Armin Straub, James WanExperimental Mathematics — Volume 22, Number 1, 2013, Pages 1-14

## 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 $$W_4(\pm 1)$$ are given and two new conjectures are recorded.

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## BibTeX

@article{walks2-2013,
author = {Jonathan M. Borwein and Armin Straub and James Wan},
title = {Three-step and four-step random walk integrals},
journal = {Experimental Mathematics},
year = {2013},
volume = {22},
number = {1},
pages = {1--14},
doi = {10.1080/10586458.2013.748379},
}