Meixner–Pollaczek polynomials and the Heisenberg algebra
Meixner–Pollaczek polynomials and the Heisenberg algebra
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Meixner–Pollaczek 多项式和海森堡代数
DOI：
10.1063/1.528394
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发表时间：
1988
影响因子：
1.3
通讯作者：
T. Koornwinder
中科院分区：
文献类型：
--
作者：
T. Koornwinder
对于连续哈恩多项式系统与海森堡代数中对称元素恒等式之间的联系，给出了另一种证明，这是由Bender， Mead和Pinsky[物理学]首先观察到的。Rev. Lett. 56,2445 (1986)；j .数学。物理学报，28,509（1987）。连续的Hahn多项式是mexner - pollaczek多项式。利用了拉格尔多项式和迈克斯纳-波拉切克多项式之间的联系，拉格尔多项式的罗德里格斯公式，一个涉及迈克斯纳-波拉切克多项式的运算公式，以及三维海森堡群不可约酉表示的薛定谔模型。
An alternative proof is given for the connection between a system of continuous Hahn polynomials and identities for symmetric elements in the Heisenberg algebra, which was first observed by Bender, Mead, and Pinsky [Phys. Rev. Lett. 56, 2445 (1986); J. Math. Phys. 28, 509 (1987)]. The continuous Hahn polynomials turn out to be Meixner–Pollaczek polynomials. Use is made of the connection between Laguerre polynomials and Meixner–Pollaczek polynomials, the Rodrigues formula for Laguerre polynomials, an operational formula involving Meixner–Pollaczek polynomials, and the Schrodinger model for the irreducible unitary representations of the three‐dimensional Heisenberg group.