查看“︁大q雅可比多项式”︁的源代码

{{NoteTA
|G1=Math
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'''大q-雅可比多项式'''（{{lang-en|Big q-Jacobi polynomials}}）是一个以[[基本超几何函数]]定义的正交多项式<ref name=r>Roelof p438</ref>：
[[File:BIG Q JACOBI 2D Maple PLOT.gif|thumb|BIG Q JACOBI 2D Maple PLOT]]
:<math>\displaystyle   P_n(x;a,b,c;q)={}_3\phi_2(q^{-n},abq^{n+1},x;aq,cq;q,q) </math>

==正交性==
大q-雅可比多项式满足下列正交关系

<math>\sum_x(p_n(x)*p_m(x)|x|v_x=h_n*\delta_mn</math>
==极限关系==
;大q雅可比多项式→[[大q拉盖尔多项式]]
令大q雅可比多项式中的<math>b =0</math>,即得大q拉盖尔多项式

<math>P_{n}(x;a,0,c;q)=P_{n}(x;a,c;q)</math>

==图集==
{|
|[[File:BIG Q JACOBI ABS COMPLEX3D Maple PLOT2.gif|thumb|BIG Q JACOBI ABS COMPLEX3D Maple PLOT2]]
|[[File:BIG Q JACOBI IM COMPLEX3D Maple PLOT.gif|thumb|BIG Q JACOBI IM COMPLEX3D Maple PLOT]]
|[[File:BIG Q JACOBI RE COMPLEX3D Maple PLOT.gif|thumb|BIG Q JACOBI RE COMPLEX3D Maple PLOT]]
|}
{|
|[[File:BIG Q JACOBI ABS COMPLEX DENSITY Maple PLOT.gif|thumb|BIG Q JACOBI ABS COMPLEX DENSITY Maple PLOT]]
|[[File:BIG Q JACOBI IM COMPLEX DENSITY Maple PLOT.gif|thumb|BIG Q JACOBI IM COMPLEX DENSITY Maple PLOT]]
|[[File:BIG Q JACOBI RE COMPLEX DENSITY Maple PLOT.gif|thumb|BIG Q JACOBI RE COMPLEX DENSITY Maple PLOT]]
|}

==参考文献==
*{{Citation | last1=Andrews | first1=George E. |authorlink1=George Andrews (mathematician)| last2=Askey | first2=Richard |authorlink2=Richard Askey | editor1-last=Brezinski | editor1-first=C. | editor2-last=Draux | editor2-first=A. | editor3-last=Magnus | editor3-first=Alphonse P. | editor4-last=Maroni | editor4-first=Pascal | editor5-last=Ronveaux | editor5-first=A. | title=Polynômes orthogonaux et applications.  Proceedings of the Laguerre symposium held at Bar-le-Duc, October 15–18, 1984.  | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Lecture Notes in Math. | isbn=978-3-540-16059-5  | mr=838970 | year=1985 | volume=1171 | chapter=Classical orthogonal polynomials | doi=10.1007/BFb0076530 | pages=36–62}}
*{{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|title=|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:基本超幾何函數]]