Application of a composition of generating functions for obtaining explicit formulas of polynomials

Using notions of composita and composition of generating functions, we obtain explicit formulas for the Chebyshev polynomials, the Legendre polynomials, the Gegenbauer polynomials, the Associated Laguerre polynomials, the Stirling polynomials, the Abel polynomials, the Bernoulli Polynomials of the Second Kind, the Generalized Bernoulli polynomials, the Euler Polynomials, the Peters polynomials, and the Narumi polynomials.