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Experimental Mathematics Volume 22, 2013 - Issue 1
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Original Articles

Three-Step and Four-Step Random Walk Integrals

Jonathan M. Borwein CARMA, University of Newcastle, University Drive, Callaghan, NSW, 2308, Australia
,
Armin Straub Tulane University, 6823 St. Charles Avenue, New Orleans, LA, 70118, USA
&
James Wan CARMA, University of Newcastle, University Drive, Callaghan, NSW, 2308, Australia
Pages 1-14 | Published online: 18 Mar 2013
 
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Abstract

We investigate the moments of 3-step and 4-step uniform random walks in the plane. In particular, we further analyze a formula conjectured in [CitationBorwein et al. 11] expressing 4-step moments in terms of 3-step moments. Diverse related results including hypergeometric and elliptic closed forms for W 4(±1) are given, and two new conjectures are recorded.

2000 AMS Subject Classification:

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