双Q克拉夫楚克多项式

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]

${\displaystyle K_{n}(\lambda (x);c,N|q)=_{3}\Phi _{2}(q^{-n},q^{-x},cq^{x-N};q^{-N},0|q;q)}$

• 令Q拉卡多项式中${\displaystyle a=b}$,${\displaystyle cq=q^{-N}}$ 即得双Q克拉夫楚克多项式
• 令双q哈恩多项式中${\displaystyle d=c\gamma ^{-1}q^{-N-1}}$,且${\displaystyle \gamma }$→0,即得双Q克拉夫楚克多项式
• 令双Q克拉夫楚克多项式${\displaystyle c=1=p^{-1}}$,并令q→1,即得克拉夫楚克多项式

• Gasper, George; Rahman, Mizan, Basic hypergeometric series, Encyclopedia of Mathematics and its Applications 96 2nd, Cambridge University Press, 2004, ISBN 978-0-521-83357-8, MR 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 978-3-642-05013-8, MR 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 |contribution-url=缺少标题 (帮助), Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (编), NIST Handbook of Mathematical Functions, Cambridge University Press, 2010, ISBN 978-0521192255, MR2723248 

1. ^ Roelof Koekoek, p505