雙Q克拉夫楚克多項式

雙Q克拉夫楚克多項式是一個以基本超幾何函數定義的正交多項式

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

關係式

• 令Q拉卡多項式中$a=b$,$cq=q^{-N}$ 即得雙Q克拉夫楚克多項式
• 令雙q哈恩多項式中$d=c\gamma ^{-1}q^{-N-1}$,且$\gamma$→0,即得雙Q克拉夫楚克多項式
• 令雙Q克拉夫楚克多項式$c=1=p^{-1}$,並令q→1,即得克拉夫楚克多項式

圖集

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

參考文獻

• 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, Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (編), NIST Handbook of Mathematical Functions, Cambridge University Press, 2010, ISBN 978-0521192255, MR2723248