DLMF:19.9.E2 (Q6245): 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
 
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.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11808 / rank
 
Normal rank
Property / Symbols used: Q11808 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11808 / qualifier
 
xml-id: C19.S1.XMD5.m1adec
Property / Symbols used
 
Property / Symbols used: Q11815 / rank
 
Normal rank
Property / Symbols used: Q11815 / qualifier
 
test:

k superscript 𝑘 {\displaystyle{\displaystyle k^{\prime}}}

k^{\prime}
Property / Symbols used: Q11815 / qualifier
 
xml-id: C19.S1.XMD6.m1adec

Latest revision as of 12:44, 2 January 2020

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DLMF:19.9.E2
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    Statements

    1 + k 2 8 < K ( k ) ln ( 4 / k ) < 1 + k 2 4 , 1 superscript superscript 𝑘 2 8 complete-elliptic-integral-first-kind-K 𝑘 4 superscript 𝑘 1 superscript superscript 𝑘 2 4 {\displaystyle{\displaystyle 1+\frac{{k^{\prime}}^{2}}{8}<\frac{K\left(k\right% )}{\ln\left(4/k^{\prime}\right)}<1+\frac{{k^{\prime}}^{2}}{4},}}
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    K ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    C19.S2.E8.m1aadec
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    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2aadec
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C19.S1.XMD5.m1adec
    0 references
    k superscript 𝑘 {\displaystyle{\displaystyle k^{\prime}}}
    C19.S1.XMD6.m1adec
    0 references