DLMF:27.5.E5 (Q8029): Difference between revisions

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

μ ⁡ ( n ) Moebius-mu 𝑛 {\displaystyle{\displaystyle\mu\left(\NVar{n}\right)}}

\Moebiusmu@{\NVar{n}}
Property / Symbols used: Möbius function / qualifier
 
xml-id: C27.S2.E12.m2acdec

Revision as of 14:18, 2 January 2020

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DLMF:27.5.E5
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    Statements

    Defining formula
    ln ⁡ n = ∑ d | n Λ ⁡ ( d ) ⟺ Λ ⁡ ( n ) = ∑ d | n ( ln ⁡ d ) ⁢ μ ⁡ ( n d ) . ⟺ 𝑛 subscript divides 𝑑 𝑛 Mangoldt-Lambda 𝑑 Mangoldt-Lambda 𝑛 subscript divides 𝑑 𝑛 𝑑 Moebius-mu 𝑛 𝑑 {\displaystyle{\displaystyle\ln n=\sum_{d\mathbin{|}n}\Lambda\left(d\right)% \Longleftrightarrow\Lambda\left(n\right)=\sum_{d\mathbin{|}n}(\ln d)\mu\left(% \frac{n}{d}\right).}}
    0 references
    DLMF id
    DLMF:27.5.E5
    0 references
    Symbols used
    Mangoldt’s function
    Defining formula
    Λ ⁡ ( n ) Mangoldt-Lambda 𝑛 {\displaystyle{\displaystyle\Lambda\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E14.m2adec
    0 references
    Möbius function
    Defining formula
    μ ⁡ ( n ) Moebius-mu 𝑛 {\displaystyle{\displaystyle\mu\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E12.m2acdec
    0 references
     
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