DLMF:4.9.E2 (Q1610): 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.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1adec

Latest revision as of 18:13, 1 January 2020

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DLMF:4.9.E2
No description defined

    Statements

    Defining formula
    ln ⁡ ( 1 + z 1 - z ) = 2 ⁢ z 1 - z 2 3 - 4 ⁢ z 2 5 - 9 ⁢ z 2 7 - 16 ⁢ z 2 9 - ⁢ ⋯ , 1 𝑧 1 𝑧 continued-fraction 2 𝑧 1 continued-fraction superscript 𝑧 2 3 continued-fraction 4 superscript 𝑧 2 5 continued-fraction 9 superscript 𝑧 2 7 continued-fraction 16 superscript 𝑧 2 limit-from 9 ⋯ {\displaystyle{\displaystyle\ln\left(\frac{1+z}{1-z}\right)=\cfrac{2z}{1-% \cfrac{z^{2}}{3-\cfrac{4z^{2}}{5-\cfrac{9z^{2}}{7-\cfrac{16z^{2}}{9-}}}}}% \cdots,}}
    0 references
    DLMF id
    DLMF:4.9.E2
    0 references
    Symbols used
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1adec
    0 references
     
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