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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