DLMF:27.11.E4 (Q8073): Difference between revisions

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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.m2abdec
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.m1cdec
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.m1cdec

Latest revision as of 14:25, 2 January 2020

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DLMF:27.11.E4
No description defined

    Statements

    Defining formula
    ∑ n ≤ x σ 1 ⁡ ( n ) = π 2 12 ⁢ x 2 + O ⁡ ( x ⁢ ln ⁡ x ) . subscript 𝑛 𝑥 divisor-sigma 1 𝑛 2 12 superscript 𝑥 2 Big-O 𝑥 𝑥 {\displaystyle{\displaystyle\sum_{n\leq x}\sigma_{1}\left(n\right)=\frac{{\pi^% {2}}}{12}x^{2}+O\left(x\ln x\right).}}
    0 references
    DLMF id
    DLMF:27.11.E4
    0 references
    constraint
    x ≥ 2 𝑥 2 {\displaystyle{\displaystyle x\geq 2}}
    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.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    sum of powers of divisors of $$n$$
    Defining formula
    σ α ⁡ ( n ) divisor-sigma 𝛼 𝑛 {\displaystyle{\displaystyle\sigma_{\NVar{\alpha}}\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E10.m2adec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
    0 references
    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1cdec
    0 references
    Q12237
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C27.S1.XMD6.m1cdec
    0 references
     
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