Derivations and identities for the Chebyshev polynomials
Abstract
UDC 519.114; 512.622We 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.
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