Formula:KLS:14.24:02

<< Formula:KLS:14.24:01

formula in Al-Salam-Carlitz I

Formula:KLS:14.24:03 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \int_a^1\qPochhammer{qx,a^{-1}qx}{q}{\infty}\AlSalamCarlitzI{a}{m}@{x}{q}\AlSalamCarlitzI{a}{n}@{x}{q}\,d_qx {}=(-a)^n(1-q)\qPochhammer{q}{q}{n}\qPochhammer{q,a,a^{-1}q}{q}{\infty}q^{\binomial{n}{2}}\,\Kronecker{m}{n} }}

Constraint(s)

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

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 (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 U^{(n)}_{\alpha}}}  : Al-Salam-Carlitz I polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamCarlitzI
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \binom{n}{k}}}  : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#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 14.24 of KLS.

URL links

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<< Formula:KLS:14.24:01

formula in Al-Salam-Carlitz I

Formula:KLS:14.24:03 >>