DLMF:1.2.E6} (Q35): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10756 / rank
 
Normal rank
Property / Symbols used: Q10756 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q10756 / qualifier
 
xml-id: C1.S1.XMD4.m1adec

Revision as of 15:46, 1 January 2020

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DLMF:1.2.E6}
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    Statements

    Defining formula
    ( z k ) = z ⁢ ( z - 1 ) ⁢ ⋯ ⁢ ( z - k + 1 ) k ! = ( - 1 ) k ⁢ ( - z ) k k ! = ( - 1 ) k ⁢ ( k - z - 1 k ) . binomial 𝑧 𝑘 𝑧 𝑧 1 ⋯ 𝑧 𝑘 1 𝑘 superscript 1 𝑘 Pochhammer 𝑧 𝑘 𝑘 superscript 1 𝑘 binomial 𝑘 𝑧 1 𝑘 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{z}{k}=\frac{z(z-1)\cdots(z% -k+1)}{k!}=\frac{(-1)^{k}{\left(-z\right)_{k}}}{k!}=(-1)^{k}\genfrac{(}{)}{0.0% pt}{}{k-z-1}{k}.}}
    0 references
    DLMF id
    DLMF:1.2.E6}
    0 references
    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1aedec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    Q10760
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C1.S1.XMD1.m1dec
    0 references
    Q10756
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C1.S1.XMD4.m1adec
    0 references
     
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