  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.
