Sigmoid functions and exponential Riordan arrays

Paul Barry

    Research output: Contribution to journalArticlepeer-review

    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.
    Original languageEnglish
    Journaln/a
    Publication statusUnpublished - 2017

    Keywords

    • sigmoid function, special functions, exponential Riordan array, orthogonal polynomials, Hankel transform, generating functions

    Fingerprint

    Dive into the research topics of 'Sigmoid functions and exponential Riordan arrays'. Together they form a unique fingerprint.

    Cite this