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Koepf","submitted_at":"2021-10-25T22:33:35Z","abstract_excerpt":"Consider $\\{p_n\\}_{n=0}^{\\infty}$, a sequence of polynomials orthogonal with respect to $w(x)>0$ on $(a,b)$, and polynomials $\\{g_{n,k}\\}_{n=0}^{\\infty},k \\in \\mathbb{N}_0$, orthogonal with respect to $c_k(x)w(x)>0$ on $(a,b)$, where $c_{k}(x)$ is a polynomial of degree $k$ in $x$. We show how Christoffel's formula can be used to obtain mixed three-term recurrence equations involving the polynomials $p_n$, $p_{n-1}$ and $g_{n-m,k},m\\in\\{2,3,\\dots, n-1\\}$. 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