DLMF:18.28.E16 (Q5991): Difference between revisions

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‎Created a new Item: Wikidata Toolkit example test item creation
 
‎Changed an Item: Add constraint
 
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Property / Symbols defined
 
Property / Symbols defined: continuous $$q$$ -Hermite polynomial / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2agdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expe}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2agdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2ahdec
Property / Symbols used
 
Property / Symbols used: Q11298 / rank
 
Normal rank
Property / Symbols used: Q11298 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{\NVar{a}}{\NVar{q}}{\NVar{n}}}

\qPochhammer{\NVar{a}}{\NVar{q}}{\NVar{n}}
Property / Symbols used: Q11298 / qualifier
 
xml-id: C17.S2.SS1.p1.m2akdec
Property / Symbols used
 
Property / Symbols used: basic hypergeometric (or $$q$$ -hypergeometric) function / rank
 
Normal rank
Property / Symbols used: basic hypergeometric (or $$q$$ -hypergeometric) function / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{\NVar{r+1}}{\NVar{s}}@{\NVar{a_{0},\dots,a_{r}}}{\NVar{b_{1},\dots,b_{s}}}{\NVar{q}}{\NVar{z}}}

\qgenhyperphi{\NVar{r+1}}{\NVar{s}}@{\NVar{a_{0},\dots,a_{r}}}{\NVar{b_{1},\dots,b_{s}}}{\NVar{q}}{\NVar{z}}
Property / Symbols used: basic hypergeometric (or $$q$$ -hypergeometric) function / qualifier
 
xml-id: C17.S4.E1.m2aedec
Property / Symbols used
 
Property / Symbols used: Q11728 / rank
 
Normal rank
Property / Symbols used: Q11728 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q}

q
Property / Symbols used: Q11728 / qualifier
 
xml-id: C18.S1.XMD3.m1mdec
Property / Symbols used
 
Property / Symbols used: Q11744 / rank
 
Normal rank
Property / Symbols used: Q11744 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell}

\ell
Property / Symbols used: Q11744 / qualifier
 
xml-id: C18.S1.XMD4.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1kdec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1fdec

Latest revision as of 12:23, 2 January 2020

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DLMF:18.28.E16
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \contqHermitepolyH{n}@{\cos@@{\theta}}{q}=\sum_{\ell=0}^{n}\frac{\qPochhammer{q}{q}{n}e^{\iunit(n-2\ell)\theta}}{\qPochhammer{q}{q}{\ell}\qPochhammer{q}{q}{n-\ell}}=e^{\iunit n\theta}\qgenhyperphi{2}{0}@@{q^{-n},0}{-}{q}{q^{n}e^{-2\iunit\theta}}.}
    0 references
    DLMF id
    DLMF:18.28.E16
    0 references
    Symbols used
    cosine function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\NVar{z}}}
    xml-id
    C4.S14.E2.m2agdec
    0 references
    base of natural logarithm
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expe}
    xml-id
    C4.S2.E11.m2agdec
    0 references
    imaginary unit
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit}
    xml-id
    C1.S9.E1.m2ahdec
    0 references
    Q11298
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{\NVar{a}}{\NVar{q}}{\NVar{n}}}
    xml-id
    C17.S2.SS1.p1.m2akdec
    0 references
    basic hypergeometric (or $$q$$ -hypergeometric) function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{\NVar{r+1}}{\NVar{s}}@{\NVar{a_{0},\dots,a_{r}}}{\NVar{b_{1},\dots,b_{s}}}{\NVar{q}}{\NVar{z}}}
    xml-id
    C17.S4.E1.m2aedec
    0 references
    Q11728
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q}
    xml-id
    C18.S1.XMD3.m1mdec
    0 references
    Q11744
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell}
    xml-id
    C18.S1.XMD4.m1ddec
    0 references
    Q11726
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n}
    xml-id
    C18.S1.XMD6.m1kdec
    0 references
    Q11727
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x}
    xml-id
    C18.S2.XMD3.m1fdec
    0 references
     
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