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

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

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

参考文献

• 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. (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