Volume 22, Issue 3, June 2015, Pages 374 - 380
On some connections between the Gompertz function and special numbers
Authors
Grzegorz Rządkowski*
Department of Finance and Risk Management, Warsaw University of Technology, Ludwika Narbutta 85 00-999 Warsaw, Poland.g.rzadkowski@wz.pw.edu.pl
Wojciech Rządkowski
Faculty of Physics, University of Warsaw, Hoża 69 00-681 Warsaw, Poland
Faculty of Electronics and Information Technology, Warsaw University of Technology, Nowowiejska 15/19 00-665 Warsaw, Poland.wojciech.rzadkowski@gmail.com
Paweł Wójcicki
Faculty of Mathematics and Computer Science, Warsaw University of Technology, Koszykowa 75 00-662 Warsaw, Poland.p.wojcicki@mini.pw.edu.pl
*corresponding author.
Corresponding Author
Grzegorz Rządkowski
Received 14 March 2015, Accepted 3 June 2015, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2015.1079419How to use a DOI?
- Keywords
- Gompertz function; Gumbel distribution; Bernoulli numbers; Stirling numbers of the second kind
- Abstract
In the present paper we show that the Gompertz function, the Fisher–Tippett and the Gumbel probability distributions are related to both Stirling numbers of the second kind and Bernoulli numbers. Especially we prove for the Gumbel probability density function an analog of the Grosset–Veselov formula which connects 1-soliton solution of the KdV equation with Bernoulli numbers.
- Copyright
- © 2015 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Grzegorz Rządkowski AU - Wojciech Rządkowski AU - Paweł Wójcicki PY - 2021 DA - 2021/01/06 TI - On some connections between the Gompertz function and special numbers JO - Journal of Nonlinear Mathematical Physics SP - 374 EP - 380 VL - 22 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2015.1079419 DO - 10.1080/14029251.2015.1079419 ID - Rządkowski2021 ER -