Chinese Physics Letters, 36, 7, 070201.

**ISSN/ISBN:** Not available at this time.
**DOI:** 10.1088/0256-307X/36/7/070201

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**Abstract:** The first digit law, also known as Benford's law or the significant digit law, is an empirical
phenomenon that the leading digit of numbers from real world sources favors small ones in a form
$\log(1+{1}/{d})$, where $d=1, 2, ..., 9$. Such a law keeps elusive for over one hundred years
because it was obscure whether this law is due to the logical consequence of the number system or
some mysterious mechanism of the nature. We provide a simple and elegant proof of this law from the application of the Laplace transform, which is an important tool of mathematical methods in physics. We reveal that the first digit law is originated from the basic property of the number system, thus it should be attributed as a basic mathematical knowledge for wide applications.

**Bibtex:**

```
@article{,
author = {Mingshu Cong and Bo-Qiang Ma},
title = {A Proof of First Digit Law from Laplace Transform},
year = {2019},
journal = {Chinese Physics Letters},
volume = {36},
number = {7},
eid = {070201},
pages = {070201},
url = {http://cpl.iphy.ac.cn/EN/abstract/article_105355.shtml},
doi = {10.1088/0256-307X/36/7/070201}
}
```

**Reference Type:** Journal Article

**Subject Area(s):** Analysis