DLMF:25.8.E9 (Q7666): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12150 / rank
 
Normal rank
Property / Symbols used: Q12150 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12150 / qualifier
 
xml-id: C25.S1.XMD1.m1hdec

Latest revision as of 13:34, 2 January 2020

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DLMF:25.8.E9
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    Statements

    Defining formula
    ∑ k = 1 ∞ ζ ⁡ ( 2 ⁢ k ) ( 2 ⁢ k + 1 ) ⁢ 2 2 ⁢ k = 1 2 - 1 2 ⁢ ln ⁡ 2 . superscript subscript 𝑘 1 Riemann-zeta 2 𝑘 2 𝑘 1 superscript 2 2 𝑘 1 2 1 2 2 {\displaystyle{\displaystyle\sum_{k=1}^{\infty}\frac{\zeta\left(2k\right)}{(2k% +1)2^{2k}}=\frac{1}{2}-\frac{1}{2}\ln 2.}}
    0 references
    DLMF id
    DLMF:25.8.E9
    0 references
    Symbols used
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2ahdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
    0 references
    Q12150
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1hdec
    0 references
     
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