DLMF:27.4.E3 (Q8014): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12234 / rank
 
Normal rank
Property / Symbols used: Q12234 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12234 / qualifier
 
xml-id: C27.S1.XMD4.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12235 / rank
 
Normal rank
Property / Symbols used: Q12235 / qualifier
 
Defining formula:

p , p 1 , … 𝑝 subscript 𝑝 1 … {\displaystyle{\displaystyle p,p_{1},\ldots}}

p,p_{1},\ldots
Property / Symbols used: Q12235 / qualifier
 
xml-id: C27.S1.XMD5.m1bdec

Latest revision as of 14:16, 2 January 2020

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DLMF:27.4.E3
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    Statements

    Defining formula
    ζ ⁡ ( s ) = ∑ n = 1 ∞ n - s = ∏ p ( 1 - p - s ) - 1 , Riemann-zeta 𝑠 superscript subscript 𝑛 1 superscript 𝑛 𝑠 subscript product 𝑝 superscript 1 superscript 𝑝 𝑠 1 {\displaystyle{\displaystyle\zeta\left(s\right)=\sum_{n=1}^{\infty}n^{-s}=% \prod_{p}(1-p^{-s})^{-1},}}
    0 references
    DLMF id
    DLMF:27.4.E3
    0 references
    constraint
    ℜ ⁡ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
    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.m2adec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1bdec
    0 references
    Q12235
    Defining formula
    p , p 1 , … 𝑝 subscript 𝑝 1 … {\displaystyle{\displaystyle p,p_{1},\ldots}}
    xml-id
    C27.S1.XMD5.m1bdec
    0 references
     
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