Obtaining Chebyshev Polynomials Properties, Lucas Symbolic Formula by Hyperdifferential Operators

Abstract

This work shows that properties of each kind of Chebyshev polynomials may be obtained from a hyper-differential operator applying on a monomial and a symbolic formula \(Tn(x)=: cos\hat{B}\ x^n =:(C+x)^n\) .  It also exposes a new approach for obtaining generating functions of them by operator calculus built from the derivative and the positional operators.