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On two lattices with interlacing nodes, we consider discrete measures for which a point weight is determined by the product of two classical Meixner weight functions. Although such a system of measures and corresponding multiple orthogonal polynomials were already known, this system does not belong to any of the known general classes of perfect systems, namely, it is neither an Angelesco system nor an AT system. For this system, we prove perfectness and also write the difference Pearson equation. We also obtain a generalization of the Rodrigues formula for all the indices. Similar results hold for the product of two Kravchuk weights. Our proof of perfectness relies on an intriguing hypergeometric identity.

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A Curious Hypergeometric Identity and Perfectness of Meixner–Sorokin System of Weights

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  • 发表日期：

    2025年

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  • Alexander I. Aptekarev,
  • Alexander V. Dyachenko,
  • Vladimir G. Lysov

摘要

On two lattices with interlacing nodes, we consider discrete measures for which a point weight is determined by the product of two classical Meixner weight functions. Although such a system of measures and corresponding multiple orthogonal polynomials were already known, this system does not belong to any of the known general classes of perfect systems, namely, it is neither an Angelesco system nor an AT system. For this system, we prove perfectness and also write the difference Pearson equation. We also obtain a generalization of the Rodrigues formula for all the indices. Similar results hold for the product of two Kravchuk weights. Our proof of perfectness relies on an intriguing hypergeometric identity.