DLMF:27.6.E2 (Q8034): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
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.m1dec

Latest revision as of 14:19, 2 January 2020

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DLMF:27.6.E2
No description defined

    Statements

    Defining formula
    ∑ d | n μ ⁡ ( d ) ⁢ f ⁢ ( d ) = ∏ p | n ( 1 - f ⁢ ( p ) ) , subscript divides 𝑑 𝑛 Moebius-mu 𝑑 𝑓 𝑑 subscript product divides 𝑝 𝑛 1 𝑓 𝑝 {\displaystyle{\displaystyle\sum_{d\mathbin{|}n}\mu\left(d\right)f(d)=\prod_{p% \mathbin{|}n}(1-f(p)),}}
    0 references
    DLMF id
    DLMF:27.6.E2
    0 references
    constraint
    n > 1 𝑛 1 {\displaystyle{\displaystyle n>1}}
    0 references
    Symbols used
    Möbius function
    Defining formula
    μ ⁡ ( n ) Moebius-mu 𝑛 {\displaystyle{\displaystyle\mu\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E12.m2adec
    0 references
    Q12241
    Defining formula
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C27.S1.XMD1.m1adec
    0 references
    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1adec
    0 references
    Q12235
    Defining formula
    p , p 1 , … 𝑝 subscript 𝑝 1 … {\displaystyle{\displaystyle p,p_{1},\ldots}}
    xml-id
    C27.S1.XMD5.m1dec
    0 references
     
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