DLMF:25.8.E6 (Q7663): 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.m1edec

Revision as of 13:33, 2 January 2020

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DLMF:25.8.E6
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    Statements

    Defining formula
    ∑ k = 0 ∞ ζ ⁡ ( 2 ⁢ k ) ⁢ z 2 ⁢ k = - 1 2 ⁢ π ⁢ z ⁢ cot ⁡ ( π ⁢ z ) , superscript subscript 𝑘 0 Riemann-zeta 2 𝑘 superscript 𝑧 2 𝑘 1 2 𝜋 𝑧 𝜋 𝑧 {\displaystyle{\displaystyle\sum_{k=0}^{\infty}\zeta\left(2k\right)z^{2k}=-% \tfrac{1}{2}\pi z\cot\left(\pi z\right),}}
    0 references
    DLMF id
    DLMF:25.8.E6
    0 references
    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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    Symbols used
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    cotangent function
    Defining formula
    cot ⁡ z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}
    xml-id
    C4.S14.E7.m2adec
    0 references
    Q12150
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1edec
    0 references
     
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