Lattice paths and branched continued fractions: An infinite sequence of generalizations of the Stieltjes--Rogers and Thron--Rogers polynomials, with coefficientwise Hankel-total positivity

Mathias Pétréolle, Alan D. Sokal, Bao-Xuan Zhu

We define an infinite sequence of generalizations, parametrized by an integer $m\ge 1$, of the Stieltjes--Rogers and Thron--Rogers polynomials; they arise as the power-series expa…