Benford solutions of linear difference equations. (English) Zbl 1318.39001

AlSharawi, Ziyad (ed.) et al., Theory and applications of difference equations and discrete dynamical systems. ICDEA, Muscat, Oman, May 26–30, 2013. Berlin: Springer (ISBN 978-3-662-44139-8/hbk; 978-3-662-44140-4/ebook). Springer Proceedings in Mathematics & Statistics 102, 23-60 (2014).
Summary: Benford’s Law (BL), a notorious gem of mathematics folklore, asserts that leading digits of numerical data are usually not equidistributed, as might be expected, but rather follow one particular logarithmic distribution. Since first recorded by S. Newcomb in 1881 [Sylv., Am. J. IV, 39–41 (1881; JFM 13.0161.01)], this apparently counter-intuitive phenomenon has attracted much interest from scientists and mathematicians alike. This article presents a comprehensive overview of the theory of BL for autonomous linear difference equations. Necessary and sufficient conditions are given for solutions of such equations to conform to BL in its strongest form. The results extend and unify previous results in the literature. Their scope and limitations are illustrated by numerous instructive examples.
For the entire collection see [Zbl 1297.39001].


39A06 Linear difference equations


JFM 13.0161.01
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