Formula:KLS:14.01:21

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q^{-n}(1-q^n)(1-abcdq^{n-1}){\mathcal P}_n(z) {}=A(z){\mathcal P}_n(qz)-\left[A(z)+A(z^{-1})\right]{\mathcal P}_n(z)+A(z^{-1}){\mathcal P}_n(q^{-1}z) }}

Substitution(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle A(z)=\frac{(1-az)(1-bz)(1-cz)(1-dz)}{(1-z^2)(1-qz^2)}}} &
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle {\mathcal P}_n(z):=\frac{\qPochhammer{ab,ac,ad}{q}{n}}{a^n}\,\qHyperrphis{4}{3}@@{q^{-n},abcdq^{n-1},az,az^{-1}}{ab,ac,ad}{q}{q}}}


Proof

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Symbols List

& : logical and
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 {{}_{r}\phi_{s}}}}  : basic hypergeometric (or Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -hypergeometric) function : http://dlmf.nist.gov/17.4#E1

Bibliography

Equation in Section 14.1 of KLS.

URL links

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