Year: 2017
Type: preprint
Abstract: Sigmoid functions play an important role in many areas of applied mathematics, including machine learning, population dynamics and probability. We place the study of sigmoid functions in the context of the derivative sub-group of the group of exponential Riordan arrays. Links to families of polynomials are drawn, and it is shown that in some cases these polynomials are orthogonal. In the non-orthogonal case, transformations are given that produce orthgonal systems. Alternative means of characterisation are given, based on the production (Stieltjes) matrix associated to the relevant Riordan array.
Source: arXiv (Cornell University)
Author: Barry, Paul
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2589951767