查看“︁斯蒂尔吉斯-维格特多项式”︁的源代码


[[File:Stieltjes-Wigert polynomails.gif|thumb|Stieltjes-Wigert polynomails]]
'''斯蒂尔吉斯-维格特多项式'''是一个以[[基本超几何函数]]定义的[[正交多项式]]

:<math>\displaystyle   S_n(x;q) = \frac{1}{(q;q)_n)}{}_1\phi_1(q^{-n},0;q,-q^{n+1}x) </math>

==极限关系==
;[[Q拉盖尔多项式]]→斯蒂尔吉斯-维格特多项式

<math>\lim_{\alpha  \to  \infty}(xq^{-\alpha};q)=S_{n}(x;q)</math>



;[[Q贝塞尔多项式]]→斯蒂尔吉斯-维格特多项式



;[[Q查理耶多项式]]→斯蒂尔吉斯-维格特多项式


;斯蒂尔吉斯-维格特多项式→[[埃尔米特多项式]]

==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=Koekoek | first1=Roelof | last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Springer Monographs in Mathematics | isbn=978-3-642-05013-8 | doi=10.1007/978-3-642-05014-5 | mr=2656096 | year=2010}}
*{{dlmf|title=Ch. 18, Orthogonal polynomials|url=http://dlmf.nist.gov/18|first=Tom H. |last=Koornwinder|first2=Roderick S. C.|last2= Wong|first3=Roelof |last3=Koekoek||first4=René F. |last4=Swarttouw}}
*{{Citation | last1=Szegő | first1=Gábor | title=Orthogonal Polynomials | publisher=Colloquium Publications 23, American Mathematical Society, Fourth Edition| isbn=978-0-8218-1023-1 | mr=0372517 | year=1975}}
*{{Citation | last1=Stieltjes | first1=T. -J. | title=Recherches sur les fractions continues | url=http://www.numdam.org/numdam-bin/item?id=AFST_1995_6_4_1_J1_0 | language=fr | jfm=25.0326.01 | mr=1344720 | year=1894 | journal=Ann. Fac. Sci. Toulouse | volume=VIII | pages=1–122 | accessdate=2015-02-07 | archive-date=2015-02-07 | archive-url=https://web.archive.org/web/20150207031954/http://www.numdam.org/numdam-bin/item?id=AFST_1995_6_4_1_J1_0 | dead-url=no }}
*{{Citation | last1=Wigert | first1=S. | title=Sur les polynomes orthogonaux et l'approximation des fonctions continues | language=fr | jfm=49.0296.01 | year=1923 | journal=Arkiv för matematik, astronomi och fysik | volume=17 | pages=1–1}}
[[Category:正交多项式]]