Q查理耶多项式

q查理耶多项式是一个以基本超几何函数定义的正交多项式

极限关系

令Q查理耶多项式 a→a*(1-q),并令q→1,即得查理耶多项式

 

验证Q查理耶多项式→查理耶多项式

Q查理耶多项式之第4项(k=4):


  展开之:  

另一方面 查理耶多项式的k=4项为

 

展开之

 

二者显然相等 QED

图集

 
Q-CHARLIER ABS COMPLEX 3D MAPLE PLOT
 
Q-CHARLIER IM COMPLEX 3D MAPLE PLOT
 
Q-CHARLIER RE COMPLEX 3D MAPLE PLOT
 
Q-CHARLIER ABS DENSITY MAPLE PLOT
 
Q-CHARLIER IM DENSITY MAPLE PLOT
 
Q-CHARLIER 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 |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