Multiple orthogonal polynomials associated with branched continued fractions for ratios of hypergeometric series
Multiple orthogonal polynomials associated with branched continued fractions for ratios of hypergeometric series
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与超几何级数比率的分支连分数相关的多个正交多项式
DOI：
10.1016/j.aam.2023.102505
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发表时间：
2023
影响因子：
1.1
通讯作者：
Lima H
中科院分区：
文献类型：
--
作者：
Lima H
本文研究的主要对象是连续超几何级数和II型多重正交多项式在阶跃线上的比关于其矩为Pochhammer符号乘积比的线性泛函或测度的分支连分式表示。这是最近发现的多重正交多项式与分支连分式之间的联系的一个有趣的案例研究，给出了一个清楚的例子，说明这种联系如何导致这两个主题的相当大的进展。我们首先获得了关于格路的生成多项式和矩阵的全正性的新结果，并对多重正交多项式与分支连分式之间的联系的一般理论作出了新的贡献。连分数，重点是它的应用，分析多个正交多项式。然后，我们构造了新的分支连分式的比连续超几何级数。我们给出了这些分支连续分数的系数的正性的条件，我们表明，Pochhammer符号的产品的比率是生成多项式的格路径的一个特殊情况下的分支连续分数的研究。接下来，我们引入一个家庭的II型多重正交多项式的阶梯线与这些分支连分数。给出了这类多项式的终止超几何级数公式，研究了它们的微分性质，并得到了它们满足的显式递推关系。最后，我们把多重正交多项式的分析集中到相应的分支连分式系数都为正的情形。在这些情况下，正交性条件可以用Meijer G-函数的正真实的直线上的测度来表示，并且我们得到了关于多项式零点位置和渐近性态的结果.这里研究的多重正交多项式包括经典的Laguerre正交多项式、Jacobi正交多项式和Bessel正交多项式，关于包含修正Bessel函数、合流超几何函数和Gauss超几何函数的两测度Nikishin系统的多重正交多项式，和关于Meijer G-函数的多重正交多项式，用于研究Ginibre随机矩阵乘积的奇异值，以及Jacobi-函数的任意正整数和特殊情况下具有常递归系数的ar-正交多项式序列，皮涅托多项式
The main objects of the investigation presented in this paper are branched-continued-fraction representations of ratios of contiguous hypergeometric series and type II multiple orthogonal polynomials on the step-line with respect to linear functionals or measures whose moments are ratios of products of Pochhammer symbols. This is an interesting case study of the recently found connection between multiple orthogonal polynomials and branched continued fractions that gives a clear example of how this connection leads to considerable advances on both topics.We start by obtaining new results about generating polynomials of lattice paths and total positivity of matrices and giving new contributions to the general theory of the connection between multiple orthogonal polynomials and branched continued fractions with emphasis on its application to the analysis of multiple orthogonal polynomials. Then, we construct new branched continued fractions for ratios of contiguous hypergeometric series. We give conditions for positivity of the coefficients of these branched continued fractions and we show that the ratios of products of Pochhammer symbols are generating polynomials of lattice paths for a special case of the branched continued fractions under study. Next, we introduce a family of type II multiple orthogonal polynomials on the step-line associated with those branched continued fractions. We present a formula as terminating hypergeometric series for these polynomials, we study their differential properties, and we find an explicit recurrence relation satisfied by them. Finally, we focus the analysis of the multiple orthogonal polynomials to the cases where the corresponding branched-continued-fraction coefficients are all positive. In those cases, the orthogonality conditions can be written using measures on the positive real line involving Meijer G-functions and we obtain results about the location of the zeros and the asymptotic behaviour of the polynomials.Specialisations of the multiple orthogonal polynomials studied here include the classical Laguerre, Jacobi, and Bessel orthogonal polynomials, multiple orthogonal polynomials with respect to Nikishin systems of two measures involving modified Bessel functions, confluent hypergeometric functions, and Gauss' hypergeometric function, and multiple orthogonal polynomials with respect to Meijer G-functions used to investigate the singular values of products of Ginibre random matrices as well as ar-orthogonal polynomial sequence with constant recurrence coefficients for any positive integerrand particular instances of the Jacobi-Piñeiro polynomials.
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影响因子：
0.7
作者：
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通讯作者：
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与汇合超几何函数相关的多个正交多项式
影响因子：
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作者：
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Ana F. Loureiro
DOI：
10.1090/s0002-9947-08-04535-2
发表时间：
2006-06
影响因子：
1.3
作者：
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通讯作者：
Els Coussement;J. Coussement;W. Assche
影响因子：
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DOI：
--
发表时间：
2014
期刊：
影响因子：
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作者：
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通讯作者：
W. Assche