Formula:KLS:14.12:15

<< Formula:KLS:14.12:14

formula in Little q-Jacobi

Formula:KLS:14.12:17 >>

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

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 (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:14.12:14

formula in Little q-Jacobi

Formula:KLS:14.12:17 >>