DLMF:27.4.E7 (Q8018): 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.m1fdec

Latest revision as of 14:17, 2 January 2020

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DLMF:27.4.E7
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    Statements

    Defining formula
    ∑ n = 1 ∞ λ ⁡ ( n ) ⁢ n - s = ζ ⁡ ( 2 ⁢ s ) ζ ⁡ ( s ) , superscript subscript 𝑛 1 Liouville-lambda 𝑛 superscript 𝑛 𝑠 Riemann-zeta 2 𝑠 Riemann-zeta 𝑠 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}\lambda\left(n\right)n^{-s}=% \frac{\zeta\left(2s\right)}{\zeta\left(s\right)},}}
    0 references
    DLMF id
    DLMF:27.4.E7
    0 references
    constraint
    ℜ ⁡ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
    0 references
    Symbols used
    Liouville’s function
    Defining formula
    λ ⁡ ( n ) Liouville-lambda 𝑛 {\displaystyle{\displaystyle\lambda\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E13.m2adec
    0 references
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2acdec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1acdec
    0 references
    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1fdec
    0 references
     
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