Derivations and identities for the Chebyshev polynomials - Bedratyuk , L. P.; Lunio, N. B. (Ukrains’kyi Matematychnyi Zhurnal, 2021)
UDC 519.114; 512.622 We introduce the notion of Chebyshev derivations of the first and second kinds based on the polynomial algebra and corresponding specific differential operators, derive the elements of their kernels, and prove that any element of the kernel of the derivations defines a polynomial identity for Chebyshev polynomials of both kinds. We obtain several polynomial identities involving the Chebyshev polynomials of both kinds, a partial case of the Jacobi polynomials, and the generalized hypergeometric function.