Pseudo-involutions in the Riordan group and Chebyshev polynomials

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.