Hyperdifferential and Symbolic Representations of Chebyshev Polynomials
New Frontiers in Physical Science Research Vol. 8,
22 February 2023
,
Page 71-86
https://doi.org/10.9734/bpi/nfpsr/v8/18456D
Abstract
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 \(\partial\)x and the “multiply by x” operators instead of fastidious summations.
- Hyperdifferential aspect of gegenbauer polynomials
- symbolic formulae and generating functions of chebyshev polynomials by operator calculus