DLMF:24.6.E5 (Q7469): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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.m1ddec

Revision as of 01:31, 2 January 2020

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DLMF:24.6.E5
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    Statements

    Defining formula
    E 2 ⁢ n = 1 2 n - 1 ⁢ ∑ k = 0 n - 1 ( - 1 ) n - k ⁢ ( n - k ) 2 ⁢ n ⁢ ∑ j = 0 k ( 2 ⁢ n - 2 ⁢ j k - j ) ⁢ 2 j , Euler-number-E 2 𝑛 1 superscript 2 𝑛 1 superscript subscript 𝑘 0 𝑛 1 superscript 1 𝑛 𝑘 superscript 𝑛 𝑘 2 𝑛 superscript subscript 𝑗 0 𝑘 binomial 2 𝑛 2 𝑗 𝑘 𝑗 superscript 2 𝑗 {\displaystyle{\displaystyle E_{2n}=\frac{1}{2^{n-1}}\sum_{k=0}^{n-1}(-1)^{n-k% }(n-k)^{2n}\*\sum_{j=0}^{k}{2n-2j\choose k-j}2^{j},}}
    0 references
    DLMF id
    DLMF:24.6.E5
    0 references
    Symbols used
    Q11238
    Defining formula
    E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}
    xml-id
    C24.S2.SS2.m1aadec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1addec
    0 references
    Q12116
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C24.S1.XMD1.m1ddec
    0 references
     
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