DLMF:27.5.E6 (Q8030): Difference between revisions

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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.m2addec
Property / Symbols used
 
Property / Symbols used: Q12234 / rank
 
Normal rank
Property / Symbols used: Q12234 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12234 / qualifier
 
xml-id: C27.S1.XMD4.m1edec
Property / Symbols used
 
Property / Symbols used: Q12237 / rank
 
Normal rank
Property / Symbols used: Q12237 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12237 / qualifier
 
xml-id: C27.S1.XMD6.m1dec
Property / Symbols used
 
Property / Symbols used: Q12250 / rank
 
Normal rank
Property / Symbols used: Q12250 / qualifier
 
Defining formula:

F ⁢ ( s ) 𝐹 𝑠 {\displaystyle{\displaystyle F(s)}}

F(s)
Property / Symbols used: Q12250 / qualifier
 
xml-id: C27.S5.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q12251 / rank
 
Normal rank
Property / Symbols used: Q12251 / qualifier
 
Defining formula:

G ⁢ ( s ) 𝐺 𝑠 {\displaystyle{\displaystyle G(s)}}

G(s)
Property / Symbols used: Q12251 / qualifier
 
xml-id: C27.S5.XMD2.m1dec

Latest revision as of 14:18, 2 January 2020

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DLMF:27.5.E6
No description defined

    Statements

    Defining formula
    G ⁢ ( x ) = ∑ n ≤ x F ⁢ ( x n ) ⟺ F ⁢ ( x ) = ∑ n ≤ x μ ⁡ ( n ) ⁢ G ⁢ ( x n ) , ⟺ 𝐺 𝑥 subscript 𝑛 𝑥 𝐹 𝑥 𝑛 𝐹 𝑥 subscript 𝑛 𝑥 Moebius-mu 𝑛 𝐺 𝑥 𝑛 {\displaystyle{\displaystyle G(x)=\sum_{n\leq x}F\left(\frac{x}{n}\right)% \Longleftrightarrow F(x)=\sum_{n\leq x}\mu\left(n\right)G\left(\frac{x}{n}% \right),}}
    0 references
    DLMF id
    DLMF:27.5.E6
    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.m2addec
    0 references
    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1edec
    0 references
    Q12237
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C27.S1.XMD6.m1dec
    0 references
    Q12250
    Defining formula
    F ⁢ ( s ) 𝐹 𝑠 {\displaystyle{\displaystyle F(s)}}
    xml-id
    C27.S5.XMD1.m1dec
    0 references
    Q12251
    Defining formula
    G ⁢ ( s ) 𝐺 𝑠 {\displaystyle{\displaystyle G(s)}}
    xml-id
    C27.S5.XMD2.m1dec
    0 references
     
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