Q克拉夫楚克多项式

q克拉夫楚克多项式是以基本超几何函数定义的正交多项式^[1]

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

图集

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

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
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