### Berger, A and Eshun, G (2014)

#### Benford solutions of linear difference equations

Theory and Applications of Difference Equations and Discrete Dynamical Systems, Springer Proceedings in Mathematics & Statistics Volume 102, pp. 23-60.

**ISSN/ISBN:** 978-3-662-44139-8
**DOI:** 10.1007/978-3-662-44140-4_2

**Abstract:** Benfordâ€™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 Newcomb in 1881, 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.

**Bibtex:**

```
@incollection{
year={2014},
isbn={978-3-662-44139-8},
booktitle={Theory and Applications of Difference Equations and Discrete Dynamical Systems},
volume={102},
series={Springer Proceedings in Mathematics & Statistics},
editor={AlSharawi, Ziyad and Cushing, Jim M. and Elaydi, Saber},
doi={10.1007/978-3-662-44140-4_2},
title={Benford Solutions of Linear Difference Equations},
url={http://dx.doi.org/10.1007/978-3-662-44140-4_2},
publisher={Springer Berlin Heidelberg},
author={Berger, Arno and Eshun, Gideon},
pages={23-60},
language={English}
}
```

**Reference Type:** Book Chapter

**Subject Area(s):** Dynamical Systems