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DLMF:25.11.E11 - MaRDI portal

DLMF:25.11.E11 (Q8378)

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DLMF:25.11.E11
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    Statements

    DLMF defining formula
    ζ ⁡ ( s , 1 2 ) = ( 2 s - 1 ) ⁢ ζ ⁡ ( s ) , Hurwitz-zeta 𝑠 1 2 superscript 2 𝑠 1 Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(s,\tfrac{1}{2}\right)=(2^{s}-1)\zeta% \left(s\right),}}
    0 references
    constraint
    s ≠ 1 𝑠 1 {\displaystyle{\displaystyle s\neq 1}}
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    Symbols used
    Hurwitz zeta function
    DLMF defining formula
    ζ ⁡ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S11.E1.m2aldec
    0 references
    Riemann zeta function
    DLMF defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2abdec
    0 references
    complex variable
    DLMF defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C25.S1.XMD7.m1jdec
    0 references
     
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