离散q-埃尔米特多项式 是以超几何函数 定义的正交多项式 [1]
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{\displaystyle \displaystyle h_{n}(x;q)=q^{\binom {n}{2}}{}_{2}\phi _{1}(q^{-n},x^{-1};0;q,-qx)=x^{n}{}_{2}\phi _{0}(q^{-n},q^{-n+1};;q^{2},q^{2n-1}/x^{2})=U_{n}^{(-1)}(x;q)}
图集
DISCRETE Q-HERMITE I ABS COMPLEX 3D MAPLE PLOT
DISCRETE Q-HERMITE I IM COMPLEX 3D MAPLE PLOT
DISCRETE Q-HERMITE I RE COMPLEX 3D MAPLE PLOT
DISCRETE Q-HERMITE I ABS DENSITY MAPLE PLOT
DISCRETE Q-HERMITE I IM DENSITY MAPLE PLOT
DISCRETE Q-HERMITE I RE DENSITY MAPLE PLOT
参考文献
Roelof Koekoek, p547-549,Springer 2010
Berg, Christian; Ismael, Mourad, Q-Hermite Polynomials and Classical Orthogonal Polynomials [1] , 1994
Al-Salam, W. A.; Carlitz, L. , Some orthogonal q-polynomials, Mathematische Nachrichten , 1965, 30 : 47–61, ISSN 0025-584X , MR 0197804 , doi:10.1002/mana.19650300105
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 , MR 2723248