DLMF:18.28.E7 (Q5982): Difference between revisions
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imported>Admin Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
imported>Admin Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
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| Property / Symbols used | |||
| Property / Symbols used: Askey–Wilson polynomial / rank | |||
Normal rank | |||
| Property / Symbols used: Askey–Wilson polynomial / qualifier | |||
test: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AskeyWilsonpolyp{\NVar{n}}@{\NVar{x}}{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{d}}% {\NVar{q}}}\AskeyWilsonpolyp{\NVar{n}}@{\NVar{x}}{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{d}}% {\NVar{q}} | |||
| Property / Symbols used: Askey–Wilson polynomial / qualifier | |||
xml-id: C18.S28.E1.m2aadec | |||
Revision as of 13:20, 2 January 2020
No description defined
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | DLMF:18.28.E7 |
No description defined |
Statements
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AlSalamChiharapolyQ{n}@{\cos@@{\theta}}{a}{b}{q}=\AskeyWilsonpolyp{n}@{\cos@@{\theta}}{a}{b}{0}{0}{q}=a^{-n}\sum_{\ell=0}^{n}q^{\ell}\frac{\qPochhammer{abq^{\ell}}{q}{n-\ell}\qPochhammer{q^{-n}}{q}{\ell}}{\qPochhammer{q}{q}{\ell}}\*\prod_{j=0}^{\ell-1}(1-2aq^{j}\cos@@{\theta}+a^{2}q^{2j})=\frac{\qPochhammer{ab}{q}{n}}{a^{n}}\qgenhyperphi{3}{2}@@{q^{-n},ae^{\iunit\theta},ae^{-\iunit\theta}}{ab,0}{q}{q}=\qPochhammer{be^{-\iunit\theta}}{q}{n}e^{\iunit n\theta}\qgenhyperphi{2}{1}@@{q^{-n},ae^{\iunit\theta}}{b^{-1}q^{1-n}e^{\iunit\theta}}{q}{b^{-1}qe^{-\iunit\theta}}.}
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