Consider an n-dimensional space with metric of signature \((p_+,q_ -)\) and let \(f_ k(x^ 1,...,x^ n)\) be a homogeneous polynomial. Then, by isomorphism, a symmetric tensor \(f^{\alpha_ 1,...,\alpha_ k}\) is associated with \(f_ k\). Also, let the classical orthogonal polynomials be written in the form \[ (*)\quad {\mathcal F}_ k(x)=\sum^{[k/2]}_{p=0}F_{k-2p}x^{k-2p}. \] Then, by establishing the image of the monomial \(x^{k-2p}\), which is essentially \(\Delta^ p(x^{\alpha_ 1}...x^{\alpha_ k})\), the author obtains an analogue of (*) for the corresponding symmetric tensor \({\mathcal F}^{\alpha_ 1,...,\alpha_ k}\); this is the so-called covariant expression of the polynomial \({\mathcal F}_ k(x)\). Other sums involving polynomials are similarly treated. The author lists a considerable number of expressions involving classical orthogonal polynomials and establishes the corresponding covariant expressions.