DLMF:24.5.E1 (Q7453): Difference between revisions

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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.m1adec
Property / Symbols used
 
Property / Symbols used: Q12113 / rank
 
Normal rank
Property / Symbols used: Q12113 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12113 / qualifier
 
xml-id: C24.S1.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q12110 / rank
 
Normal rank
Property / Symbols used: Q12110 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12110 / qualifier
 
xml-id: C24.S1.XMD5.m1dec

Latest revision as of 00:29, 2 January 2020

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DLMF:24.5.E1
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    Statements

    k = 0 n - 1 ( n k ) B k ( x ) = n x n - 1 , superscript subscript 𝑘 0 𝑛 1 binomial 𝑛 𝑘 Bernoulli-polynomial-B 𝑘 𝑥 𝑛 superscript 𝑥 𝑛 1 {\displaystyle{\displaystyle\sum_{k=0}^{n-1}{n\choose k}B_{k}\left(x\right)=nx% ^{n-1},}}
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    n = 2 , 3 , 𝑛 2 3 {\displaystyle{\displaystyle n=2,3,\dots}}
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    B n ( x ) Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}
    C24.S2.SS1.m2adec
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    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    C1.S2.SS1.m1adec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C24.S1.XMD2.m1dec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C24.S1.XMD5.m1dec
    0 references