Formula:KLS:14.20:03

<< Formula:KLS:14.20:02

formula in Little q-Laguerre / Wall

Formula:KLS:14.20:04 >>

${\displaystyle{\displaystyle{\displaystyle\sum_{k=0}^{\infty}\frac{(aq)^{k}}{\left(q;q\right)_{k}}p_{m}\!\left(q^{k};a;q\right)p_{n}\!\left(q^{k};a;q\right)=\frac{(aq)^{n}}{\left(aq;q\right)_{\infty}}\frac{\left(q;q\right)_{n}}{\left(aq;q\right)_{n}}\,\delta_{m,n}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle 0<aq<1}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre / Wall polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqLaguerre
${\displaystyle{\displaystyle{\displaystyle\delta_{m,n}}}}$ : Kronecker delta : http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r4

Bibliography

Equation in Section 14.20 of KLS.

URL links

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<< Formula:KLS:14.20:02

formula in Little q-Laguerre / Wall

Formula:KLS:14.20:04 >>