查看“︁罗杰斯-斯泽格多项式”︁的源代码

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[[File:Rogers-Szego polynomials 1.gif|thumb|Rogers-Szego Polynomials]]
[[File:Rogers-Szego polynomials 2.gif|thumb|Rogers-Szego Polynomials]]
'''罗杰斯-斯泽格多项式'''（{{lang-en|Rogers–Szegő polynomials}}）是1926年匈牙利数学家斯泽格首先研究的在单位圆上的正交多项式，以[[Q阶乘幂]]定义如下；

::<math>h_n(x;q) = \sum_{k=0}^n\frac{(q;q)_n}{(q;q)_k(q;q)_{n-k}}x^k</math>


前面几个罗杰斯-斯泽格多项式为：

:<math> h_1(x;q)= 1+x              </math>
:<math> h_2(x;q)= 1+\frac{(1-q^2)*x}{(1-q)}+x^2              </math>
:<math> h_3(x;q)= 1+\frac{(1-q^3)*x}{(1-q)}+\frac{(1-q^3)*x^2}{(1-q)}+x^3              </math>
:<math> h_4(x;q)= 1+\frac{(1-q^4)*x}{(1-q)}+\frac{(1-q^3)*(1-q^4)*x^2}{((1-q)*(1-q^2))}+\frac{(1-q^4)*x^3}{(1-q)}+x^4              </math>
:<math> h_5(x;q)= 1+\frac{(1-q^5)*x}{(1-q)}+\frac{(1-q^4)*(1-q^5)*x^2}{((1-q)*(1-q^2))}+\frac{(1-q^4)*(1-q^5)*x^3}{((1-q)*(1-q^2))}+\frac{(1-q^5)*x^4}{(1-q)}+x^5              </math>

==参考文献==
*{{Citation | last1=Gasper | first1=George | last2=Rahman | first2=Mizan | title=Basic hypergeometric series | publisher=[[Cambridge University Press]] | edition=2nd | series=Encyclopedia of Mathematics and its Applications | isbn=978-0-521-83357-8 | doi=10.2277/0521833574 |mr=2128719 | year=2004 | volume=96}}
*{{Citation | last1=Szegő | first1=Gábor | title=Beitrag zur theorie der thetafunktionen | id=Reprinted in his collected papers | year=1926 | journal=Sitz Preuss. Akad. Wiss. Phys. Math. Ki. | volume=XIX | pages=242–252}}

[[Category:正交多项式]]