DLMF:25.8.E3 (Q7660): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12149 / rank
 
Normal rank
Property / Symbols used: Q12149 / qualifier
 
Defining formula:

s 𝑠 {\displaystyle{\displaystyle s}}

s
Property / Symbols used: Q12149 / qualifier
 
xml-id: C25.S1.XMD7.m1adec

Latest revision as of 13:33, 2 January 2020

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DLMF:25.8.E3
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    Statements

    Defining formula
    ∑ k = 0 ∞ ( s ) k ⁢ ζ ⁡ ( s + k ) k ! ⁢ 2 s + k = ( 1 - 2 - s ) ⁢ ζ ⁡ ( s ) , superscript subscript 𝑘 0 Pochhammer 𝑠 𝑘 Riemann-zeta 𝑠 𝑘 𝑘 superscript 2 𝑠 𝑘 1 superscript 2 𝑠 Riemann-zeta 𝑠 {\displaystyle{\displaystyle\sum_{k=0}^{\infty}\frac{{\left(s\right)_{k}}\zeta% \left(s+k\right)}{k!2^{s+k}}=(1-2^{-s})\zeta\left(s\right),}}
    0 references
    DLMF id
    DLMF:25.8.E3
    0 references
    constraint
    s ≠ 1 𝑠 1 {\displaystyle{\displaystyle s\neq 1}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2abdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    Q12150
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1bdec
    0 references
    Q12149
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C25.S1.XMD7.m1adec
    0 references
     
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