DLMF:27.5.E8 (Q8032): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q12241 / rank
 
Normal rank
Property / Symbols used: Q12241 / qualifier
 
Defining formula:

d 𝑑 {\displaystyle{\displaystyle d}}

d
Property / Symbols used: Q12241 / qualifier
 
xml-id: C27.S1.XMD1.m1edec

Revision as of 14:19, 2 January 2020

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DLMF:27.5.E8
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    Statements

    Defining formula
    g ⁢ ( n ) = ∏ d | n f ⁢ ( d ) ⟺ f ⁢ ( n ) = ∏ d | n ( g ⁢ ( n d ) ) μ ⁡ ( d ) . ⟺ 𝑔 𝑛 subscript product divides 𝑑 𝑛 𝑓 𝑑 𝑓 𝑛 subscript product divides 𝑑 𝑛 superscript 𝑔 𝑛 𝑑 Moebius-mu 𝑑 {\displaystyle{\displaystyle g(n)=\prod_{d\mathbin{|}n}f(d)\Longleftrightarrow f% (n)=\prod_{d\mathbin{|}n}\left(g\left(\frac{n}{d}\right)\right)^{\mu\left(d% \right)}.}}
    0 references
    DLMF id
    DLMF:27.5.E8
    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.m2afdec
    0 references
    Q12241
    Defining formula
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C27.S1.XMD1.m1edec
    0 references
     
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