DLMF:26.3.E7 (Q7780): Difference between revisions

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Property / constraint
 

m n 0 𝑚 𝑛 0 {\displaystyle{\displaystyle m\geq n\geq 0}}

m\geq n\geq 0
Property / constraint: m n 0 𝑚 𝑛 0 {\displaystyle{\displaystyle m\geq n\geq 0}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10754 / rank
 
Normal rank
Property / Symbols used: Q10754 / qualifier
 
test:

( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

\binom{\NVar{m}}{\NVar{n}}
Property / Symbols used: Q10754 / qualifier
 
xml-id: C1.S2.SS1.m1ahdec
Property / Symbols used
 
Property / Symbols used: Q12174 / rank
 
Normal rank
Property / Symbols used: Q12174 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12174 / qualifier
 
xml-id: C26.S1.XMD4.m1dec
Property / Symbols used
 
Property / Symbols used: Q12171 / rank
 
Normal rank
Property / Symbols used: Q12171 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12171 / qualifier
 
xml-id: C26.S1.XMD5.m1hdec
Property / Symbols used
 
Property / Symbols used: Q12172 / rank
 
Normal rank
Property / Symbols used: Q12172 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12172 / qualifier
 
xml-id: C26.S1.XMD6.m1hdec

Latest revision as of 00:08, 2 January 2020

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DLMF:26.3.E7
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    Statements

    ( m + 1 n + 1 ) = k = n m ( k n ) , binomial 𝑚 1 𝑛 1 superscript subscript 𝑘 𝑛 𝑚 binomial 𝑘 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{m+1}{n+1}=\sum_{k=n}^{m}% \genfrac{(}{)}{0.0pt}{}{k}{n},}}
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    m n 0 𝑚 𝑛 0 {\displaystyle{\displaystyle m\geq n\geq 0}}
    0 references
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    C1.S2.SS1.m1ahdec
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C26.S1.XMD4.m1dec
    0 references
    m 𝑚 {\displaystyle{\displaystyle m}}
    C26.S1.XMD5.m1hdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C26.S1.XMD6.m1hdec
    0 references