DLMF:24.14.E10 (Q7555): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12115 / rank
 
Normal rank
Property / Symbols used: Q12115 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12115 / qualifier
 
xml-id: C24.S1.XMD4.m1adec
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.m1idec

Latest revision as of 01:47, 2 January 2020

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DLMF:24.14.E10
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    Statements

    Defining formula
    ∑ ( 2 ⁢ n ) ! ( 2 ⁢ j ) ! ⁢ ( 2 ⁢ k ) ! ⁢ ( 2 ⁢ ℓ ) ! ⁢ ( 2 ⁢ m ) ! ⁢ B 2 ⁢ j ⁢ B 2 ⁢ k ⁢ B 2 ⁢ ℓ ⁢ B 2 ⁢ m = - ( 2 ⁢ n + 3 3 ) ⁢ B 2 ⁢ n - 4 3 ⁢ n 2 ⁢ ( 2 ⁢ n - 1 ) ⁢ B 2 ⁢ n - 2 . 2 𝑛 2 𝑗 2 𝑘 2 ℓ 2 𝑚 Bernoulli-number-B 2 𝑗 Bernoulli-number-B 2 𝑘 Bernoulli-number-B 2 ℓ Bernoulli-number-B 2 𝑚 binomial 2 𝑛 3 3 Bernoulli-number-B 2 𝑛 4 3 superscript 𝑛 2 2 𝑛 1 Bernoulli-number-B 2 𝑛 2 {\displaystyle{\displaystyle\sum\frac{(2n)!}{(2j)!(2k)!(2\ell)!(2m)!}B_{2j}B_{% 2k}B_{2\ell}B_{2m}=-{2n+3\choose 3}B_{2n}-\frac{4}{3}n^{2}(2n-1)B_{2n-2}.}}
    0 references
    DLMF id
    DLMF:24.14.E10
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1aedec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1agdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
    0 references
    Q12116
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C24.S1.XMD1.m1cdec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1idec
    0 references
    Q12122
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C24.S1.XMD3.m1bdec
    0 references
    Q12115
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C24.S1.XMD4.m1adec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1idec
    0 references
     
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