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We show how to define, for every Riordan group element $(g(x), f(x))$, aninvolution in the Riordan group. More generally, we show that for everypseudo-involution $P$ in the Riordan group, we can define a new involutionbeginning with an arbitrary element $(g(x), f(x))$ in the Riordan group. Wethen use this result to show that certain two-parameter families of orthogonalpolynomials defined by a Riordan array can lead to involutions in the Riordangroup, and we give an explicit form of these involutions.

A Three-parameter Family Of Involutions In The Riordan Group Defined By Orthogonal Polynomials