DLMF:27.4.E9 (Q8020): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q12233 / rank
 
Normal rank
Property / Symbols used: Q12233 / qualifier
 
Defining formula:

ν ⁡ ( n ) number-of-primes-dividing-nu 𝑛 {\displaystyle{\displaystyle\nu\left(\NVar{n}\right)}}

\nprimesdiv@{\NVar{n}}
Property / Symbols used: Q12233 / qualifier
 
xml-id: C27.S2.SS1.p1.m6adec

Revision as of 14:17, 2 January 2020

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DLMF:27.4.E9
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    Statements

    Defining formula
    ∑ n = 1 ∞ 2 ν ⁡ ( n ) ⁢ n - s = ( ζ ⁡ ( s ) ) 2 ζ ⁡ ( 2 ⁢ s ) , superscript subscript 𝑛 1 superscript 2 number-of-primes-dividing-nu 𝑛 superscript 𝑛 𝑠 superscript Riemann-zeta 𝑠 2 Riemann-zeta 2 𝑠 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}2^{\nu\left(n\right)}n^{-s}=% \frac{(\zeta\left(s\right))^{2}}{\zeta\left(2s\right)},}}
    0 references
    DLMF id
    DLMF:27.4.E9
    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.m2aedec
    0 references
    Q12233
    Defining formula
    ν ⁡ ( n ) number-of-primes-dividing-nu 𝑛 {\displaystyle{\displaystyle\nu\left(\NVar{n}\right)}}
    xml-id
    C27.S2.SS1.p1.m6adec
    0 references
     
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