Диференцiювання та тотожностi для многочленiв Чебишова

UDC 519.114; 512.622We introduce the notion of Chebyshev derivations of the first and second kinds based on the polynomial algebra andcorresponding specific differential operators, derive the elements of their kernels, and prove that any element of the kernelof the derivations defines a polynomial identity for Chebyshev polynomials of both kinds. We obtain several polynomialidentities involving the Chebyshev polynomials of both kinds, a partial case of the Jacobi polynomials, and the generalizedhypergeometric function.