On a family of 2-variable orthogonal Krawtchouk polynomials.
On a family of 2-variable orthogonal Krawtchouk polynomials.
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关于 2 变量正交 Krawtchouk 多项式族。
DOI：
10.3842/sigma.2010.090
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发表时间：
2010
影响因子：
0.9
通讯作者：
Mizan Rahman
中科院分区：
文献类型：
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作者：
F. Grunbaum;Mizan Rahman
我们给出了一个超几何证明，其中涉及Hoare和Rahman（SIGMA 4（2008），089，18页）早期获得的一系列2变量Krawtchouk多项式作为量子角动量理论的9 j符号的极限，并且被证明是对应于“扑克骰子”类型概率模型的转移概率核的本征函数。本文的证明导出并利用了正交性的充要条件来建立正交性，并指出了它们的几何意义。我们还得到了这些多项式所满足的5项递推关系。
We give a hypergeometric proof involving a family of 2-variable Krawtchouk polynomials that were obtained earlier by Hoare and Rahman (SIGMA 4 (2008), 089, 18 pages) as a limit of the 9 j symbols of quantum angular momentum theory, and shown to be eigenfunctions of the transition probability kernel corresponding to a "poker dice" type probability model. The proof in this paper derives and makes use of the necessary and sufficient conditions of orthogonality in establishing orthogonality as well as indicating their geometrical significance. We also derive a 5-term recurrence relation satisfied by these polynomials.
多元 Krawtchouk 多项式的正交关系
DOI：
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发表时间：
2011
期刊：
SIGMA
影响因子：
--
作者：
Atsushi Ishii;Yeonhee Jang;Kanako Oshiro;Atsushi Ishii;Atsushi Ishii;Atsushi Ishii;Atsushi Ishii;石井敦;Keiichi Sakai;Keiichi Sakai;山口祥司;山口祥司;境圭一;境圭一;境圭一;境圭一;境圭一;境圭一;Tetsuya Hosaka;Tetsuya Hosaka;Naotsugu Chinen and Tetsuya Hosaka;Tetsuya Hosaka;Hiroshi Mizukawa;Hiroshi Mizukawa;Tetsuya Hosaka;Hiroshi Mizukawa
通讯作者：
Hiroshi Mizukawa