Formula:KLS:14.07:04

<< Formula:KLS:14.07:03

formula in Dual q-Hahn

Formula:KLS:14.07:05 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle -\left(1-q^{-x}\right)\left(1-\gamma\delta q^{x+1}\right)\dualqHahn{n}@@{\mu(x)}{\gamma}{\delta}{N}{q} {}=A_n\dualqHahn{n+1}@@{\mu(x)}{\gamma}{\delta}{N}{q}-\left(A_n+C_n\right)\dualqHahn{n}@@{\mu(x)}{\gamma}{\delta}{N}{q}+C_n\dualqHahn{n-1}@@{\mu(x)}{\gamma}{\delta}{N}{q} }}

Substitution(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mu(x)=q^{-x}+\gamma\delta q^{x+1} =q^{-x}+q^{x+\gamma+\delta+1} =q^{-x}+\gamma\delta q^{x+1}}} &

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mu(n)=q^{-n}+\alpha\beta q^{n+1}}} &
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle C_n=\gamma q\left(1-q^n\right)\left(\delta -q^{n-N-1}\right)}} &
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle A_n=\left(1-q^{n-N}\right)\left(1-\gamma q^{n+1}\right)}} &
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mu(x):=q^{-x}+\gamma\delta q^{x+1}}} &
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mu(x)=q^{-x}+\gamma\delta q^{x+1} =q^{-x}+q^{x+\gamma+\delta+1} =q^{-x}+\gamma\delta q^{x+1}}} &

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mu(n)=q^{-n}+\alpha\beta q^{n+1}}}

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

Bibliography

Equation in Section 14.7 of KLS.

URL links

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<< Formula:KLS:14.07:03

formula in Dual q-Hahn

Formula:KLS:14.07:05 >>