DLMF:25.2.E3 (Q7598): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12148 / rank
 
Normal rank
Property / Symbols used: Q12148 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12148 / qualifier
 
xml-id: C25.S1.XMD3.m1bdec
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.m1bdec

Latest revision as of 13:20, 2 January 2020

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DLMF:25.2.E3
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    Statements

    Defining formula
    ζ ⁡ ( s ) = 1 1 - 2 1 - s ⁢ ∑ n = 1 ∞ ( - 1 ) n - 1 n s , Riemann-zeta 𝑠 1 1 superscript 2 1 𝑠 superscript subscript 𝑛 1 superscript 1 𝑛 1 superscript 𝑛 𝑠 {\displaystyle{\displaystyle\zeta\left(s\right)=\frac{1}{1-2^{1-s}}\sum_{n=1}^% {\infty}\frac{(-1)^{n-1}}{n^{s}},}}
    0 references
    DLMF id
    DLMF:25.2.E3
    0 references
    constraint
    ℜ ⁡ s > 0 𝑠 0 {\displaystyle{\displaystyle\Re s>0}}
    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.m2abdec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aadec
    0 references
    Q12148
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C25.S1.XMD3.m1bdec
    0 references
    Q12149
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C25.S1.XMD7.m1bdec
    0 references
     
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