查看“︁连续q雅可比多项式”︁的源代码


'''连续q雅可比多项式'''定义如下

<math>P_{n}^{(\alpha;\beta)}(x|q)=</math><math>\frac{(q^{\alpha+1};q)_n}{(q;q;)_n}</math>
*<math>_4\Phi_{3}</math><math>(q^{-n},q^{n+\alpha+\beta+1};q^{\alpha/2+1/4}e^{i\theta};q^{\alpha/2+1/4}e^{-i\theta})</math>

==极限关系==
;[[连续q雅可比多项式]]→[[连续q拉盖尔多项式]]

<math>\lim_{\beta \to \infty}P_{n}^{(\alpha;\beta)}(x|q)=P_{n}^{(\alpha)}(x|q)</math>

;[[连续q雅可比多项式]]→[[雅科比多项式]]
<math>\lim_{q \to 1}P_{n}^{(\alpha;\beta)}(x|q)=P_{n}^{(\alpha;\beta)}(x|q)</math>
==图集==
{|
|[[File:CONTINUOUS Q-JACOBI ABS COMPLEX 3D MAPLE PLOT.gif|thumb|CONTINUOUS Q-JACOBI ABS COMPLEX 3D MAPLE PLOT]]
|[[File:CONTINUOUS Q-JACOBI IM COMPLEX 3D MAPLE PLOT.gif|thumb|CONTINUOUS Q-JACOBI IM COMPLEX 3D MAPLE PLOT]]
|[[File:CONTINUOUS Q-JACOBI RE COMPLEX 3D MAPLE PLOT.gif|thumb|CONTINUOUS Q-JACOBI RE COMPLEX 3D MAPLE PLOT]]
|}
{|
|[[File:CONTINUOUS Q-JACOBI ABS DENSITY MAPLE PLOT.gif|thumb|CONTINUOUS Q-JACOBI ABS DENSITY MAPLE PLOT]]
|[[File:CONTINUOUS Q-JACOBI IM DENSITY MAPLE PLOT.gif|thumb|CONTINUOUS Q-JACOBI IM DENSITY MAPLE PLOT]]
|[[File:CONTINUOUS Q-JACOBI RE DENSITY MAPLE PLOT.gif|thumb|CONTINUOUS Q-JACOBI RE DENSITY MAPLE PLOT]]
|}






==参考文献==

*{{Citation | authorlink=Richard Askey | last1=Askey | first1=Richard | last2=Wilson | first2=James | title=Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials | isbn=978-0-8218-2321-7 | mr=783216 | year=1985 | journal=Memoirs of the American Mathematical Society | issn=0065-9266 | volume=54 | issue=319 | pages=iv+55|url=http://books.google.com/books?id=9q9o03nD_xsC | doi=10.1090/memo/0319}}
*{{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}}
*{{Citation | last1=Rahman | first1=Mizan | title=The linearization of the product of continuous q-Jacobi polynomials | doi=10.4153/CJM-1981-076-8 | mr=634153 | year=1981 | journal=[[Canadian Journal of Mathematics]] | issn=0008-414X | volume=33 | issue=4 | pages=961–987}}

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