DLMF:24.6.E11 (Q7475): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10754 / rank
 
Normal rank
Property / Symbols used: Q10754 / qualifier
 
Defining formula:

( 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.m1ajdec
Property / Symbols used
 
Property / Symbols used: Q12116 / rank
 
Normal rank
Property / Symbols used: Q12116 / qualifier
 
Defining formula:

j 𝑗 {\displaystyle{\displaystyle j}}

j
Property / Symbols used: Q12116 / qualifier
 
xml-id: C24.S1.XMD1.m1jdec
Property / Symbols used
 
Property / Symbols used: Q12113 / rank
 
Normal rank
Property / Symbols used: Q12113 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12113 / qualifier
 
xml-id: C24.S1.XMD2.m1jdec
Property / Symbols used
 
Property / Symbols used: Q12110 / rank
 
Normal rank
Property / Symbols used: Q12110 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12110 / qualifier
 
xml-id: C24.S1.XMD5.m1jdec

Latest revision as of 01:32, 2 January 2020

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DLMF:24.6.E11
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    Statements

    B n = n 2 n ( 2 n - 1 ) k = 1 n j = 0 k - 1 ( - 1 ) j + 1 ( n k ) j n - 1 , Bernoulli-number-B 𝑛 𝑛 superscript 2 𝑛 superscript 2 𝑛 1 superscript subscript 𝑘 1 𝑛 superscript subscript 𝑗 0 𝑘 1 superscript 1 𝑗 1 binomial 𝑛 𝑘 superscript 𝑗 𝑛 1 {\displaystyle{\displaystyle B_{n}=\frac{n}{2^{n}(2^{n}-1)}\sum_{k=1}^{n}\sum_% {j=0}^{k-1}(-1)^{j+1}{n\choose k}j^{n-1},}}
    0 references
    DLMF:24.6.E11
    0 references
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    C24.S2.SS1.m1addec
    0 references
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    C1.S2.SS1.m1ajdec
    0 references
    j 𝑗 {\displaystyle{\displaystyle j}}
    C24.S1.XMD1.m1jdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C24.S1.XMD2.m1jdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C24.S1.XMD5.m1jdec
    0 references