DLMF:24.14.E4 (Q7549): Difference between revisions

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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.m1cdec
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.m1cdec

Latest revision as of 00:46, 2 January 2020

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DLMF:24.14.E4
No description defined

    Statements

    test
    ∑ k = 0 n ( n k ) ⁢ E k ⁢ E n - k = - 2 n + 1 ⁢ E n + 1 ⁡ ( 0 ) = - 2 n + 2 ⁢ ( 1 - 2 n + 2 ) ⁢ B n + 2 n + 2 . superscript subscript 𝑘 0 𝑛 binomial 𝑛 𝑘 Euler-number-E 𝑘 Euler-number-E 𝑛 𝑘 superscript 2 𝑛 1 Euler-polynomial-E 𝑛 1 0 superscript 2 𝑛 2 1 superscript 2 𝑛 2 Bernoulli-number-B 𝑛 2 𝑛 2 {\displaystyle{\displaystyle\sum_{k=0}^{n}{n\choose k}E_{k}E_{n-k}=-2^{n+1}E_{% n+1}\left(0\right)=-2^{n+2}(1-2^{n+2})\frac{B_{n+2}}{n+2}.}}
    0 references
    DLMF id
    DLMF:24.14.E4
    0 references
    Symbols used
    Q11109
    test
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1aadec
    0 references
    Q11238
    test
    E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}
    xml-id
    C24.S2.SS2.m1adec
    0 references
    Q12114
    test
    E n ⁡ ( x ) Euler-polynomial-E 𝑛 𝑥 {\displaystyle{\displaystyle E_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS2.m2aadec
    0 references
    Q10754
    test
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1acdec
    0 references
    Q12113
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1cdec
    0 references
    Q12110
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1cdec
    0 references
     
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