DLMF:27.11.E11 (Q8080): Difference between revisions

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‎Changed an Item: Add constraint
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Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2ahdec

Revision as of 14:27, 2 January 2020

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DLMF:27.11.E11
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    Statements

    Defining formula
    ∑ p ≤ x p ≡ h ( mod k ) ln ⁡ p p = 1 ϕ ⁡ ( k ) ⁢ ln ⁡ x + O ⁡ ( 1 ) , subscript 𝑝 𝑥 modular-equivalence 𝑝 annotated ℎ pmod 𝑘 𝑝 𝑝 1 Euler-totient-phi 𝑘 𝑥 Big-O 1 {\displaystyle{\displaystyle\sum_{\begin{subarray}{c}p\leq x\\ p\equiv h\!\!\!\!\!\pmod{k}\end{subarray}}\frac{\ln p}{p}=\frac{1}{\phi\left(k% \right)}\ln x+O\left(1\right),}}
    0 references
    DLMF id
    DLMF:27.11.E11
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2ajdec
    0 references
    Euler’s totient
    Defining formula
    ϕ ⁡ ( n ) Euler-totient-phi 𝑛 {\displaystyle{\displaystyle\phi\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E7.m2acdec
    0 references
    Q12121
    Defining formula
    ≡ modular-equivalence {\displaystyle{\displaystyle\equiv}}
    xml-id
    introduction.Sx4.p2.t1.r10.m10aadec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2ahdec
    0 references
     
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