Q梅西纳多项式

Q梅西纳多项式→Q拉盖尔多项式;

令Q梅西纳多项式中${\displaystyle b=q^{\alpha }}$ ,以及${\displaystyle q^{-x}=cq^{\alpha }x}$ ,然后取${\displaystyle c\to \infty }$ 即得Q拉盖尔多项式。

${\displaystyle \lim _{c\to \infty }M_{n}(cq^{\alpha }x;q^{\alpha },c;q)={\frac {(q;q)_{n}}{(q^{\alpha +1};q)_{n}}}}$ 

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• 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 
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