Mehler-Heine asymptotics for multiple orthogonal polynomials
Mehler-Heine asymptotics for multiple orthogonal polynomials
复制标题
多个正交多项式的 Mehler-Heine 渐近
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
W. Assche
中科院分区：
文献类型：
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作者：
W. Assche
Mehler-Heine渐近描述了在支持正交测度的区间边缘附近正交多项式的行为。对于Jacobi多项式和Laguerre多项式，这种靠近硬边的渐近行为涉及到贝塞尔函数J_alpha。我们证明了多个正交多项式（其中一个）测度的区间端点附近的渐近行为涉及贝塞尔函数的推广。所考虑的多重正交多项式有Jacobi-Angelesco多项式、Jacobi-Pi~neiro多项式、多重Laguerre多项式、与修正贝塞尔函数相关的多重正交多项式（第一类和第二类）以及与Meijer $G$-函数相关的多重正交多项式。
Mehler-Heine asymptotics describe the behavior of orthogonal polynomials near the edges of the interval where the orthogonality measure is supported. For Jacobi polynomials and Laguerre polynomials this asymptotic behavior near the hard edge involves Bessel functions $J_alpha$. We show that the asymptotic behavior near the endpoint of the interval of (one of) the measures for multiple orthogonal polynomials involves a generalization of the Bessel function. The multiple orthogonal polynomials considered are Jacobi-Angelesco polynomials, Jacobi-Pi~neiro polynomials, multiple Laguerre polynomials, multiple orthogonal polynomials associated with modified Bessel functions (of the first and second kind), and multiple orthogonal polynomials associated with Meijer $G$-functions.