Q克拉夫楚克多項式

q克拉夫楚克多項式是以基本超幾何函數定義的正交多項式

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

圖集

QKrawtchouk polynomials ABS COMPLEX 3D Maple plot

QKrawtchouk polynomials IM COMPLEX 3D Maple plot

QKrawtchouk polynomials RE COMPLEX 3D Maple plot

QKrawtchouk polynomials ABS density Maple plot

QKrawtchouk polynomials im density Maple plot

QKrawtchouk 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 
• Stanton, Dennis, Three addition theorems for some q-Krawtchouk polynomials, Geometriae Dedicata, 1981, 10 (1): 403–425, ISSN 0046-5755, MR 0608153, doi:10.1007/BF01447435