DLMF:2.10.E8 (Q995): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Euler’s constant / rank
 
Normal rank
Property / Symbols used: Euler’s constant / qualifier
 
test:

γ {\displaystyle{\displaystyle\gamma}}

\EulerConstant
Property / Symbols used: Euler’s constant / qualifier
 
xml-id: C5.S2.E3.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
test:

asymptotic-expansion {\displaystyle{\displaystyle\sim}}

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11aadec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

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.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11113 / rank
 
Normal rank
Property / Symbols used: Q11113 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11113 / qualifier
 
xml-id: C2.S10.XMD3.m1fdec

Latest revision as of 16:34, 1 January 2020

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DLMF:2.10.E8
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    Statements

    j = 1 n - 1 1 j ln n + γ - 1 2 n - s = 1 B 2 s 2 s 1 n 2 s , asymptotic-expansion superscript subscript 𝑗 1 𝑛 1 1 𝑗 𝑛 1 2 𝑛 superscript subscript 𝑠 1 Bernoulli-number-B 2 𝑠 2 𝑠 1 superscript 𝑛 2 𝑠 {\displaystyle{\displaystyle\sum_{j=1}^{n-1}\frac{1}{j}\sim\ln n+\gamma-\frac{% 1}{2n}-\sum_{s=1}^{\infty}\frac{B_{2s}}{2s}\frac{1}{n^{2s}},}}
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    n 𝑛 {\displaystyle{\displaystyle n\to\infty}}
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    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    C24.S2.SS1.m1aedec
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    γ {\displaystyle{\displaystyle\gamma}}
    C5.S2.E3.m2aadec
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    asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    C2.S1.SS3.p1.m11aadec
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    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2acdec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C2.S10.XMD3.m1fdec
    0 references