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arXiv · 2502.13673

Pseudo-involutions in the Riordan group and Chebyshev polynomials

Alexander Burstein·Louis W. Shapiro
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Abstract

Generalizing the results in our previous paper, we consider pseudo-involutions in the Riordan group where the generating function $g$ for the first column of a Riordan array satisfies a functional equation of certain types involving a polynomial. For those types of equations, we find the pseudo-involutory companion of $g$. We also develop a general method for finding B-functions of Riordan pseudo-involutions in the cases we consider, and show that these B-functions involve Chebyshev polynomials. We apply our method for several families of Riordan arrays, obtaining new results and deriving known results more efficiently.

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Alexander Burstein, Louis W. Shapiro. 2025-02-19. Pseudo-involutions in the Riordan group and Chebyshev polynomials. https://arxiv.org/abs/2502.13673

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