Hyperdifferential and Symbolic Representations of Chebyshev Polynomials - Do Tan Si (New Frontiers in Physical Science Research Vol. 8, 2023)
This work shows that Chebyshev polynomials of the first kind Tn (X) and of the second kind Un (X) may be represented as the transforms of the monomial Xn each by a hyperdifferential operator so that they may be calculated easily from a symbolic formula similar to the Lucas formula for Bernoulli polynomials. It exposes also a new approach for obtaining their generating functions by operator calculus built from the derivative \(\)x and the “multiply by x” operators instead of fastidious summations.