An alternative expression for the Christoffel--Darboux formula for multiple orthogonal polynomials of mixed type is derived from the $LU$ factorization of the moment matrix of a given measure and two sets of weights. We use the action of the generalized Jacobi matrix $J$, also responsible for the recurrence relations, on the linear forms and their duals to obtain the result.

翻译：用于多种正统多式混合型的克里斯托贝尔-达尔布公式的另一种表达方式是,从某一计量尺度的瞬间矩阵和两组加权乘以1美元乘数中得出。我们使用通用的雅各比矩阵的动作($J)来获取结果,该模型还负责重现关系、线性形式及其双元。