Formula:KLS:14.25:02

<< Formula:KLS:14.25:01

formula in Al-Salam-Carlitz II

Formula:KLS:14.25:03 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \sum_{k=0}^{\infty}\frac{q^{k^2}a^k}{\qPochhammer{q}{q}{k}\qPochhammer{aq}{q}{k}} \AlSalamCarlitzII{a}{m}@{q^{-k}}{q}\AlSalamCarlitzII{a}{n}@{q^{-k}}{q} {}=\frac{\qPochhammer{q}{q}{n}a^n}{\qPochhammer{aq}{q}{\infty}q^{n^2}}\,\Kronecker{m}{n} }}

Constraint(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle 0<aq<1}}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Sigma}}  : sum : http://drmf.wmflabs.org/wiki/Definition:sum
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 V^{(n)}_{\alpha}}}  : Al-Salam-Carlitz II polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamCarlitzII
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \delta_{m,n}}}  : Kronecker delta : http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r4

Bibliography

Equation in Section 14.25 of KLS.

URL links

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<< Formula:KLS:14.25:01

formula in Al-Salam-Carlitz II

Formula:KLS:14.25:03 >>