连续q哈恩多项式

连续q-哈恩多项式基本超几何函数定义:[1]

并且

极限关系

连续q哈恩多项式Q梅西纳-帕拉泽克多项式

 

阿斯基-威尔逊多项式连续q哈恩多项式

在阿斯基-威尔逊多项式中作代换 , , , , 即得连续q哈恩多项式:  

图集

 
CONTINUOUS q hahn ABS COMPLEX3D Maple PLOT
 
CONTINUOUS q hahn IIM COMPLEX3D Maple PLOT
 
CONTINUOUS q hahn RE COMPLEX3D Maple PLOT
 
CONTINUOUS q hahn ABS densitu Maple PLOT
 
CONTINUOUS q hahn im densitu Maple PLOT
 
CONTINUOUS q hahn RE densitu 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., Chapter 18: Orthogonal Polynomials, 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 
  1. ^ Roelof, p433