DLMF:4.6.E2 (Q1571): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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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: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1adec
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 18:08, 1 January 2020

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DLMF:4.6.E2
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    Statements

    ln z = ( z - 1 z ) + 1 2 ( z - 1 z ) 2 + 1 3 ( z - 1 z ) 3 + , 𝑧 𝑧 1 𝑧 1 2 superscript 𝑧 1 𝑧 2 1 3 superscript 𝑧 1 𝑧 3 {\displaystyle{\displaystyle\ln z=\left(\frac{z-1}{z}\right)+\frac{1}{2}\left(% \frac{z-1}{z}\right)^{2}+\frac{1}{3}\left(\frac{z-1}{z}\right)^{3}+\cdots,}}
    0 references
    DLMF:4.6.E2
    0 references
    z 1 2 𝑧 1 2 {\displaystyle{\displaystyle\Re z\geq\frac{1}{2}}}
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2aadec
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    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C4.S1.XMD8.m1adec
    0 references