双Q克拉夫楚克多项式 是一个以基本超几何函数 定义的正交多项式 [ 1]
K
n
(
λ
(
x
)
;
c
,
N
|
q
)
=
3
Φ
2
(
q
−
n
,
q
−
x
,
c
q
x
−
N
;
q
−
N
,
0
|
q
;
q
)
{\displaystyle K_{n}(\lambda (x);c,N|q)=_{3}\Phi _{2}(q^{-n},q^{-x},cq^{x-N};q^{-N},0|q;q)}
令Q拉卡多项式 中
a
=
b
{\displaystyle a=b}
c
q
=
q
−
N
{\displaystyle cq=q^{-N}}
双Q克拉夫楚克多项式
令双q哈恩多项式 中
d
=
c
γ
−
1
q
−
N
−
1
{\displaystyle d=c\gamma ^{-1}q^{-N-1}}
γ
{\displaystyle \gamma }
双Q克拉夫楚克多项式
令双Q克拉夫楚克多项式
c
=
1
=
p
−
1
{\displaystyle c=1=p^{-1}}
克拉夫楚克多项式
DUAL Q-KRAWTCHOUK POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT DUAL Q-KRAWTCHOUK POLYNOMIALS IM COMPLEX 3D MAPLE PLOT DUAL Q-KRAWTCHOUK POLYNOMIALS RE COMPLEX 3D MAPLE PLOT
DUAL Q-KRAWTCHOUK POLYNOMIALS ABS DENSITY MAPLE PLOT DUAL Q-KRAWTCHOUK POLYNOMIALS IM DENSITY MAPLE PLOT DUAL Q-KRAWTCHOUK POLYNOMIALS RE DENSITY MAPLE PLOT
Gasper, George; Rahman, Mizan, Basic hypergeometric series, Encyclopedia of Mathematics and its Applications 96 2nd, Cambridge University Press , 2004, ISBN 978-0-521-83357-8MR 2128719 doi:10.2277/0521833574 Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F., Hypergeometric orthogonal polynomials and their q-analogues, Springer Monographs in Mathematics, Berlin, New York: Springer-Verlag , 2010, ISBN 978-3-642-05013-8MR 2656096 doi:10.1007/978-3-642-05014-5 Koornwinder, Tom H.; Wong, Roderick S. C.; Koekoek, Roelof; Swarttouw, René F., http://dlmf.nist.gov/18 , Olver, Frank W. J. ; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (编), NIST Handbook of Mathematical Functions , Cambridge University Press, 2010, ISBN 978-0521192255MR 2723248 
