查看“︁Q贝塞尔多项式”︁的源代码

[[File:QBessel function 2D plot.gif|thumb|qBessel function 2D plot]]
'''q-贝塞尔多项式'''，也称q-贝塞尔函数，其通过[[基本超几何函数]]定义<ref>Roelof  Koekoek, Peter Lesky  Rene Swarttouw,Hypergeometric Orthogonal Polynomials and their q-Analogues, p526 Springer 2010</ref>：


:<math>y_{n}(x;a;q)=\;_{2}\phi_1 \left(\begin{matrix} 
q^{-N} & -aq^{n} \\ 
0  \end{matrix} 
; q,qx \right) </math>

==正交关系==

<math>

\sum_{k=0}^{\infty}(\frac{a^k}{(q;q)_n}*q^{k+1 \choose 2}*y_{m}*(q^k;a;q)*y_{n}*(q^k;a;q)=(q;q)_{n}*(-aq^n;q)_{\infty}\frac{ a^{n}*q^{n+1 \choose 2} }{1+aq^{2n}   }\delta_{mn}
</math><ref name=k>Roelof  p527</ref>

==图集==
{|
|[[File:QBessel function abs complex 3D Maple plot.gif|thumb|QBessel function abs complex 3D Maple plot]]
|[[File:QBessel function Im complex 3D Maple plot.gif|thumb|QBessel function Im complex 3D Maple plot]]
|[[File:QBessel function Re complex 3D Maple plot.gif|thumb|QBessel function Re complex 3D Maple plot]]
|}
{|
|[[File:QBessel function abs density Maple plot.gif|thumb|QBessel function abs density Maple plot]]
|[[File:QBessel function Im density Maple plot.gif|thumb|QBessel function Im density Maple plot]]
|[[File:QBessel function Re density Maple plot.gif|thumb|QBessel function Re density Maple plot]]
|}

==参考文献==
<references/>

*{{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}}


[[Category:正交多项式]]
[[Category:Q-模拟]]
[[Category:特殊函数]]
[[Category:Q超几何多项式]]