Barry, Paul (2017) Sigmoid functions and exponential Riordan arrays. n/a. (Unpublished)
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | sigmoid function, special functions, exponential Riordan array, orthogonal polynomials, Hankel transform, generating functions |
| Departments or Groups: | *NONE OF THESE* |
| Divisions: | School of Science > Department of Computing, Maths and Physics |
| Depositing User: | Paul Barry |
| Date Deposited: | 03 Mar 2017 15:21 |
| Last Modified: | 23 Jun 2021 16:15 |
| URI: | https://repository.wit.ie/id/eprint/3226 |
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