On the power series of involutory functions

Alfred Schreiber

Published 2023-08-05Version 1

It is shown that the coefficients of any involutory function $f~(\neq\text{identity})$ represented as a power series can be expressed in terms of multivariable Lah polynomials. This result is based on the fact that any such $f$ can be regarded as a (compositional) conjugate of negative identity. Moreover, a constructive proof of this statement is given.