Formula:KLS:14.29:04

<< Formula:KLS:14.29:03

formula in Discrete q-Hermite II

Formula:KLS:14.29:06 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \sum_{k=-\infty}^{\infty}\left[\discrqHermiteII{m}@{cq^k}{q} \discrqHermiteII{n}@{cq^k}{q}+\discrqHermiteII{m}@{-cq^k}{q}\discrqHermiteII{n}@{-cq^k}{q}\right] w(cq^k;q)q^k {}=2\frac{\qPochhammer{q^2,-c^2q,-c^{-2}q}{q^2}{\infty}}{\qPochhammer{q,-c^2,-c^{-2}q^2}{q^2}{\infty}} \frac{\qPochhammer{q}{q}{n}}{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 c>0}}

Substitution(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle w(x;q)=\frac{1}{\qPochhammer{\iunit x,-\iunit x}{q}{\infty}}=\frac{1}{\qPochhammer{-x^2}{q^2}{\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 \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 \tilde{h}_{n}}}  : discrete Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -Hermite II polynomial : http://drmf.wmflabs.org/wiki/Definition:discrqHermiteII
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 \delta_{m,n}}}  : Kronecker delta : http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r4
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{i}}}  : imaginary unit : http://dlmf.nist.gov/1.9.i

Bibliography

Equation in Section 14.29 of KLS.

URL links

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<< Formula:KLS:14.29:03

formula in Discrete q-Hermite II

Formula:KLS:14.29:06 >>