查看“︁阿拉-萨拉姆-迟哈剌多项式”︁的源代码

[[File:AL-SALAM-CHIHARA 2D MAPLE PLOT.gif|thumb|AL-SALAM-CHIHARA 2D MAPLE PLOT]]
'''阿拉-萨拉姆-迟哈剌多项式'''(Al-Salam-Chihara polynomials)是一个以[[基本超几何函数]]定义的[[正交多项式]]<ref>Roelof KoeKoek, Hypergeometric Orthogonal Polynomials and its q-Analogues, p455,Springer 2010</ref>

<math>Q_n(x;a,b;q)=\frac{(ab;q)_{n}}{a^n}\;_{3}\phi_2\left(\begin{matrix} 
q^-n & ae^i\theta & ae^-i\theta \\ 
ab & 0  \end{matrix} 
; q,q \right)</math>

==极限关系==
阿拉-萨拉姆-迟哈剌多项式→[[连续q拉盖尔多项式]]

令[[阿拉-萨拉姆-迟哈剌多项式]] b=0,即得[[连续大Q埃尔米特多项式]]

==图集==
{|
|[[File:AL-SALAM-CHIHARA ABS COMPLEX 3D MAPLE PLOT.gif|thumb|AL-SALAM-CHIHARA ABS COMPLEX 3D MAPLE PLOT]]
|[[File:AL-SALAM-CHIHARA IM COMPLEX 3D MAPLE PLOT.gif|thumb|AL-SALAM-CHIHARA IM COMPLEX 3D MAPLE PLOT]]
|[[File:AL-SALAM-CHIHARA RE COMPLEX 3D MAPLE PLOT.gif|thumb|AL-SALAM-CHIHARA RE COMPLEX 3D MAPLE PLOT]]
|}
{|
|[[File:AL-SALAM-CHIHARA ABS DENSITY MAPLE PLOT.gif|thumb|AL-SALAM-CHIHARA ABS DENSITY MAPLE PLOT]]
|[[File:AL-SALAM-CHIHARA IM DENSITY MAPLE PLOT.gif|thumb|AL-SALAM-CHIHARA IM DENSITY MAPLE PLOT]]
|[[File:AL-SALAM-CHIHARA RE DENSITY MAPLE PLOT.gif|thumb|AL-SALAM-CHIHARA RE DENSITY MAPLE PLOT]]
|}

==参考文献==
<references/>
*{{Citation | last1=Al-Salam | first1=W. A. | last2=Chihara | first2=Theodore Seio | title=Convolutions of orthonormal polynomials | doi=10.1137/0507003 | mr=0399537 | year=1976 | journal=SIAM Journal on Mathematical Analysis | issn=0036-1410 | volume=7 | issue=1 | pages=16–28}}
*{{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|id=18.28iii|title=Al-Salam–Chihara polynomials|first=Tom H. |last=Koornwinder|first2=Roderick S. C.|last2= Wong|first3=Roelof |last3=Koekoek||first4=René F. |last4=Swarttouw}}

{{q超几何函数}}

[[Category:正交多项式]]
[[Category:Q-模拟]]
[[Category:特殊超几何函数]]