DLMF:26.10.E3 (Q7886): Difference between revisions

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‎Changed an Item: Add constraint
 
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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.m1bdec
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.m1adec
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.m1bdec
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.m1adec

Latest revision as of 13:59, 2 January 2020

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DLMF:26.10.E3
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-x)\sum_{m,n=0}^{\infty}\nrestpartitions[m]@{\leq k,\mathcal{D}}{n}x^{m}q^{n}=\sum_{m=0}^{k}\qbinom{k}{m}{q}q^{m(m+1)/2}x^{m}=\prod_{j=1}^{k}(1+x\,q^{j}),}
    0 references
    DLMF id
    DLMF:26.10.E3
    0 references
    constraint
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |x|<1}
    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.m2adec
    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.m1adec
    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.m1bdec
    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.m1adec
    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.m1bdec
    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.m1adec
    0 references
     
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