DLMF:15.12.E11 (Q5171): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2abdec
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.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11682 / rank
 
Normal rank
Property / Symbols used: Q11682 / qualifier
 
test:

ζ 𝜁 {\displaystyle{\displaystyle\zeta}}

\zeta
Property / Symbols used: Q11682 / qualifier
 
xml-id: C15.S12.XMD5.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11684 / rank
 
Normal rank
Property / Symbols used: Q11684 / qualifier
 
test:

β 𝛽 {\displaystyle{\displaystyle\beta}}

\beta
Property / Symbols used: Q11684 / qualifier
 
xml-id: C15.S12.XMD6.m1adec

Latest revision as of 14:25, 2 January 2020

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English
DLMF:15.12.E11
No description defined

    Statements

    β = ( - 3 2 ζ + 9 4 ln ( 2 + e ζ 2 + e - ζ ) ) 1 / 3 , 𝛽 superscript 3 2 𝜁 9 4 2 superscript 𝑒 𝜁 2 superscript 𝑒 𝜁 1 3 {\displaystyle{\displaystyle\beta=\left(-\frac{3}{2}\zeta+\frac{9}{4}\ln\left(% \frac{2+e^{\zeta}}{2+e^{-\zeta}}\right)\right)^{1/3},}}
    0 references
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2abdec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2abdec
    0 references
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    C15.S12.XMD5.m1ddec
    0 references
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    C15.S12.XMD6.m1adec
    0 references