Formula:KLS:14.12:17

<< Formula:KLS:14.12:15

formula in Little q-Jacobi

Formula:KLS:14.12:18 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle w(x;\alpha,\beta|q)\littleqJacobi{n}@{x}{q^{\alpha}}{q^{\beta}}{q} {}=\frac{q^{n\alpha+\binomial{n}{2}}(1-q)^n}{\qPochhammer{q^{\alpha+1}}{q}{n}} \left(\mathcal{D}_{q^{-1}}\right)^n\left[w(x;\alpha+n,\beta+n|q)\right] }}

Substitution(s)

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

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}}}  : little Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqJacobi
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 (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

Bibliography

Equation in Section 14.12 of KLS.

URL links

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<< Formula:KLS:14.12:15

formula in Little q-Jacobi

Formula:KLS:14.12:18 >>