Coefficientwise total positivity and Stieltjes moment properties from Riordan arrays

Abstract Total positivity of matrices plays an important role in various branches of mathematics. In this paper, we present some criteria for the coefficientwise total positivity of Riordan arrays and the coefficientwise Hankel‐total positivity of the row‐generating polynomial sequence of Riordan arrays. In addition, we also give some criteria for the coefficientwise Hankel‐total positivity of sequences of coefficients of compositional functions and some results for triangular convolutions preserving Stieltjes moment properties. As applications, we first obtain the coefficientwise Hankel‐total positivity of two kinds of multivariate Fuss–Narayana–Riordan polynomials, which implies those of two kinds of multivariate Fuss–Narayana polynomials proved by Pétréolle, Sokal and Zhu (Mem. Amer. Math. Soc., 2023). Then, we also derive the total positivity of Fuss–Catalan Riordan arrays, unifying total positivity results of a few well‐known combinatorial triangles.