Addendum to further results on Fermat type equations and a characterization of the Chebyshev polynomials (Q1111725)

The authors state a correction of a result concerning entire solutions of the functional equation \(f^ 2(z)+g^ 2(z)=z\) given by the authors in J. Math. Anal. Appl. 121, 317-324 (1987; Zbl 0608.30029). The assertion is, that all entire solutions are of the form \[ f(z)=(ze^{\alpha (z)}+e^{-\alpha (z)})/2;\quad g(z)=(ze^{\alpha (z)}-e^{-\alpha (z)})/2i, \] \(\alpha\) entire.