Abstract
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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Notes
In the formula for \({\beta _{0}^{J}}\) at the bottom of Table 1.1 of [5], the denominator should read Γ(α + β + 2) instead of Γ(α + β + 1).
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The work of the second author was supported in part by the Serbian Academy of Sciences and Arts (Φ-96).
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Gautschi, W., Milovanović, G.V. Orthogonal polynomials relative to a generalized Marchenko–Pastur probability measure. Numer Algor 88, 1233–1249 (2021). https://doi.org/10.1007/s11075-021-01073-1
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DOI: https://doi.org/10.1007/s11075-021-01073-1