Formula:KLS:14.11:18

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle w(x;a,b;q)\bigqLaguerre{n}@{x}{a}{b}{q} {}=\frac{a^nb^nq^{n(n+1)}(1-q)^n} {\qPochhammer{aq,bq}{q}{n}}\left(\qderiv{q}\right)^n\left[w(x;aq^n,bq^n;q)\right] }}

Substitution(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle w(x;a,b;q)=\frac{\qPochhammer{a^{-1}x,b^{-1}x}{q}{\infty}}{\qPochhammer{x}{q}{\infty}}}}


Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle P_{n}}}  : big Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:bigqLaguerre
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle (a;q)_n}}  : Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathcal{D}_q^n}}  : Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -derivative : http://drmf.wmflabs.org/wiki/Definition:qderiv

Bibliography

Equation in Section 14.11 of KLS.

URL links

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