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- W3001147961 abstract "We use Riordan array theory to give characterizations of the Borel triangle and its associated polynomial sequence. We show that the Borel polynomials are the moment sequence for a family of orthogonal polynomials whose coefficient array is a Riordan array. The role of the Catalan matrix in defining the Borel triangle is examined. We generalize the Borel triangle to a family of two parameter triangles. Generating functions are expressed as Jacobi continued fractions, as well as the zeros of appropriate quadratic expressions. The Borel triangle is exhibited as a Hadamard product of matrices. We investigate the reversions of the triangles studied. We introduce the notion of Fuss-Borel triangles and Fuss-Catalan triangles. We end with some remarks on the Catalan triangle." @default.
- W3001147961 created "2020-01-30" @default.
- W3001147961 creator A5064041323 @default.
- W3001147961 date "2020-01-23" @default.
- W3001147961 modified "2023-09-27" @default.
- W3001147961 title "Characterizations of the Borel triangle and Borel polynomials" @default.
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