DLMF:24.6.E6 (Q7470): Difference between revisions

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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.m1edec
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.m1edec
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.m1edec

Latest revision as of 01:31, 2 January 2020

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DLMF:24.6.E6
No description defined

    Statements

    Defining formula
    E 2 ⁢ n = ∑ k = 1 2 ⁢ n ( - 1 ) k 2 k - 1 ⁢ ( 2 ⁢ n + 1 k + 1 ) ⁢ ∑ j = 0 ⌊ 1 2 ⁢ k - 1 2 ⌋ ( k j ) ⁢ ( k - 2 ⁢ j ) 2 ⁢ n . Euler-number-E 2 𝑛 superscript subscript 𝑘 1 2 𝑛 superscript 1 𝑘 superscript 2 𝑘 1 binomial 2 𝑛 1 𝑘 1 superscript subscript 𝑗 0 1 2 𝑘 1 2 binomial 𝑘 𝑗 superscript 𝑘 2 𝑗 2 𝑛 {\displaystyle{\displaystyle E_{2n}=\sum_{k=1}^{2n}\frac{(-1)^{k}}{2^{k-1}}{2n% +1\choose k+1}\*\sum_{j=0}^{\left\lfloor\tfrac{1}{2}k-\tfrac{1}{2}\right% \rfloor}{k\choose j}(k-2j)^{2n}.}}
    0 references
    DLMF id
    DLMF:24.6.E6
    0 references
    Symbols used
    Q11238
    Defining formula
    E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}
    xml-id
    C24.S2.SS2.m1abdec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1aedec
    0 references
    Q11169
    Defining formula
    ⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}
    xml-id
    introduction.Sx4.p1.t1.r17.m4adec
    0 references
    Q12116
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C24.S1.XMD1.m1edec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1edec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1edec
    0 references
     
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