Formula:KLS:14.29:06

<< Formula:KLS:14.29:04

formula in Discrete q-Hermite II

Formula:KLS:14.29:07 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \int_{-\infty}^{\infty}\frac{\discrqHermiteII{m}@{x}{q}\discrqHermiteII{n}@{x}{q}}{\qPochhammer{-x^2}{q^2}{\infty}}\,d_qx =\frac{\qPochhammer{q^2,-q,-q}{q^2}{\infty}}{\qPochhammer{q^3,-q^2,-q^2}{q^2}{\infty}} \frac{\qPochhammer{q}{q}{n}}{q^{n^2}}\,\Kronecker{m}{n} }}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \int}}  : integral : http://dlmf.nist.gov/1.4#iv
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

Bibliography

Equation in Section 14.29 of KLS.

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<< Formula:KLS:14.29:04

formula in Discrete q-Hermite II

Formula:KLS:14.29:07 >>