DLMF:24.4.E8 (Q7421): Difference between revisions

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‎Changed an Item: Add constraint
 
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.m1gdec

Latest revision as of 01:25, 2 January 2020

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DLMF:24.4.E8
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    Statements

    Defining formula
    ∑ k = 1 m ( - 1 ) m - k ⁢ k n = E n ⁡ ( m + 1 ) + ( - 1 ) m ⁢ E n ⁡ ( 0 ) 2 . superscript subscript 𝑘 1 𝑚 superscript 1 𝑚 𝑘 superscript 𝑘 𝑛 Euler-polynomial-E 𝑛 𝑚 1 superscript 1 𝑚 Euler-polynomial-E 𝑛 0 2 {\displaystyle{\displaystyle\sum_{k=1}^{m}(-1)^{m-k}k^{n}=\frac{E_{n}\left(m+1% \right)+(-1)^{m}E_{n}\left(0\right)}{2}.}}
    0 references
    DLMF id
    DLMF:24.4.E8
    0 references
    Symbols used
    Q12114
    Defining formula
    E n ⁡ ( x ) Euler-polynomial-E 𝑛 𝑥 {\displaystyle{\displaystyle E_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS2.m2acdec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1adec
    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.m1gdec
    0 references
     
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