The Schett polynomials are a sequence of polynomials introduced by Dumont (1979); they are generated by a derivative operator. These polynomials unify and generalise the Taylor coefficients of the Jacobian elliptic functions sn, cn and dn.

The content of this talk is inspired by an integration-by-parts technique due to Stieltjes, Rogers and others for obtaining continued fractions. We generalise this technique and rewrite it in the language of production matrices for exponential Riordan arrays. As an application of this, we show that the two sequences of even and odd Schett polynomials are coefficientwise Hankel totally positive. (Based on ongoing joint work with Alan Sokal.)