DLMF:24.14.E7 (Q7552): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11109 / rank
 
Normal rank
Property / Symbols used: Q11109 / qualifier
 
test:

B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}

\BernoullinumberB{\NVar{n}}
Property / Symbols used: Q11109 / qualifier
 
xml-id: C24.S2.SS1.m1acdec
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.m1afdec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5adec
Property / Symbols used
 
Property / Symbols used: Q12116 / rank
 
Normal rank
Property / Symbols used: Q12116 / qualifier
 
test:

j 𝑗 {\displaystyle{\displaystyle j}}

j
Property / Symbols used: Q12116 / qualifier
 
xml-id: C24.S1.XMD1.m1dec
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.m1fdec
Property / Symbols used
 
Property / Symbols used: Q12115 / rank
 
Normal rank
Property / Symbols used: Q12115 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12115 / qualifier
 
xml-id: C24.S1.XMD4.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.m1fdec

Latest revision as of 00:46, 2 January 2020

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DLMF:24.14.E7
No description defined

    Statements

    test
    ∑ j = 0 m ∑ k = 0 n ( m j ) ⁢ ( n k ) ⁢ B j ⁢ B k m + n - j - k + 1 = ( - 1 ) m - 1 ⁢ m ! ⁢ n ! ( m + n ) ! ⁢ B m + n . superscript subscript 𝑗 0 𝑚 superscript subscript 𝑘 0 𝑛 binomial 𝑚 𝑗 binomial 𝑛 𝑘 Bernoulli-number-B 𝑗 Bernoulli-number-B 𝑘 𝑚 𝑛 𝑗 𝑘 1 superscript 1 𝑚 1 𝑚 𝑛 𝑚 𝑛 Bernoulli-number-B 𝑚 𝑛 {\displaystyle{\displaystyle\sum_{j=0}^{m}\sum_{k=0}^{n}\genfrac{(}{)}{0.0pt}{% }{m}{j}\genfrac{(}{)}{0.0pt}{}{n}{k}\frac{B_{j}B_{k}}{m+n-j-k+1}=(-1)^{m-1}% \frac{m!n!}{(m+n)!}B_{m+n}.}}
    0 references
    DLMF id
    DLMF:24.14.E7
    0 references
    Symbols used
    Q11109
    test
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1acdec
    0 references
    Q10754
    test
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1afdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q12116
    test
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C24.S1.XMD1.m1dec
    0 references
    Q12113
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1fdec
    0 references
    Q12115
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C24.S1.XMD4.m1dec
    0 references
    Q12110
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1fdec
    0 references
     
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