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DLMF:27.5.E8 - MaRDI portal

DLMF:27.5.E8 (Q8725)

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DLMF:27.5.E8
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    Statements

    DLMF 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
    Symbols used
    Möbius function
    DLMF defining formula
    μ ⁡ ( n ) Moebius-mu 𝑛 {\displaystyle{\displaystyle\mu\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E12.m2afdec
    0 references
    positive integer
    DLMF defining formula
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C27.S1.XMD1.m1edec
    0 references
    positive integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1fdec
    0 references
    function
    DLMF defining formula
    f 𝑓 {\displaystyle{\displaystyle f}}
    xml-id
    C27.S5.XMD3.m1bdec
    0 references
    function
    DLMF defining formula
    g 𝑔 {\displaystyle{\displaystyle g}}
    xml-id
    C27.S5.XMD4.m1bdec
    0 references

    Identifiers

     
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