DLMF:26.9.E7 (Q7880): 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 used
 
Property / Symbols used: $$q$$ -binomial coefficient (or Gaussian polynomial) / rank
 
Normal rank
Property / Symbols used: $$q$$ -binomial coefficient (or Gaussian polynomial) / qualifier
 
Defining formula:

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

\qbinom{\NVar{n}}{\NVar{m}}{\NVar{q}}
Property / Symbols used: $$q$$ -binomial coefficient (or Gaussian polynomial) / qualifier
 
xml-id: C17.S2.E27.m2acdec
Property / Symbols used
 
Property / Symbols used: Q12190 / rank
 
Normal rank
Property / Symbols used: Q12190 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nrestpartitions[\NVar{k}]@{\leq\NVar{m}}{\NVar{n}}}

\nrestpartitions[\NVar{k}]@{\leq\NVar{m}}{\NVar{n}}
Property / Symbols used: Q12190 / qualifier
 
xml-id: C26.S9.SS1.m1aadec
Property / Symbols used
 
Property / Symbols used: Q12173 / rank
 
Normal rank
Property / Symbols used: Q12173 / qualifier
 
Defining formula:

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

x
Property / Symbols used: Q12173 / qualifier
 
xml-id: C26.S1.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q12176 / rank
 
Normal rank
Property / Symbols used: Q12176 / qualifier
 
Defining formula:

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

j
Property / Symbols used: Q12176 / qualifier
 
xml-id: C26.S1.XMD3.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12174 / rank
 
Normal rank
Property / Symbols used: Q12174 / qualifier
 
Defining formula:

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

k
Property / Symbols used: Q12174 / qualifier
 
xml-id: C26.S1.XMD4.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12171 / rank
 
Normal rank
Property / Symbols used: Q12171 / qualifier
 
Defining formula:

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

m
Property / Symbols used: Q12171 / qualifier
 
xml-id: C26.S1.XMD5.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12172 / rank
 
Normal rank
Property / Symbols used: Q12172 / qualifier
 
Defining formula:

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

n
Property / Symbols used: Q12172 / qualifier
 
xml-id: C26.S1.XMD6.m1gdec
Property / Symbols used
 
Property / Symbols used: Q12189 / rank
 
Normal rank
Property / Symbols used: Q12189 / qualifier
 
Defining formula:

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

q
Property / Symbols used: Q12189 / qualifier
 
xml-id: C26.S9.XMD1.m1cdec

Latest revision as of 12:58, 2 January 2020

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DLMF:26.9.E7
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{m,n=0}^{\infty}\nrestpartitions[k]@{\leq m}{n}x^{k}q^{n}=1+\sum_{k=1}^{\infty}\qbinom{m+k}{k}{q}x^{k}=\prod_{j=0}^{m}\frac{1}{1-x\,q^{j}}.}
    0 references
    DLMF id
    DLMF:26.9.E7
    0 references
    Symbols used
    $$q$$ -binomial coefficient (or Gaussian polynomial)
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qbinom{\NVar{n}}{\NVar{m}}{\NVar{q}}}
    xml-id
    C17.S2.E27.m2acdec
    0 references
    Q12190
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nrestpartitions[\NVar{k}]@{\leq\NVar{m}}{\NVar{n}}}
    xml-id
    C26.S9.SS1.m1aadec
    0 references
    Q12173
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x}
    xml-id
    C26.S1.XMD1.m1dec
    0 references
    Q12176
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle j}
    xml-id
    C26.S1.XMD3.m1bdec
    0 references
    Q12174
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k}
    xml-id
    C26.S1.XMD4.m1ddec
    0 references
    Q12171
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m}
    xml-id
    C26.S1.XMD5.m1cdec
    0 references
    Q12172
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n}
    xml-id
    C26.S1.XMD6.m1gdec
    0 references
    Q12189
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q}
    xml-id
    C26.S9.XMD1.m1cdec
    0 references
     
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