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


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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    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},