The Marchenko–Pastur probability measure, of interest in the asymptotic theory of random matrices, is generalized in what appears to be a natural way. The orthogonal polynomials and their three-term recurrence relation for this generalized Marchenko–Pastur measure are obtained in explicit form, analytically as well as symbolically using Mathematica. Special cases involve Chebyshev polynomials of all four kinds. Supporting Matlab software is provided.

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相对于广义Marchenko-Pastur概率测度的正交多项式

随机矩阵渐近理论中感兴趣的Marchenko-Pastur概率测度以一种自然的方式被推广。使用Mathematica以解析形式和符号形式以显式形式获得此广义Marchenko-Pastur测度的正交多项式及其三项递归关系。特殊情况涉及所有四种Chebyshev多项式。提供了支持的Matlab软件。