DLMF:4.6.E6 (Q1575): Difference between revisions

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

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1abdec

Revision as of 18:08, 1 January 2020

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English
DLMF:4.6.E6
No description defined

    Statements

    Defining formula
    ln ⁡ ( z + a ) = ln ⁡ a + 2 ⁢ ( ( z 2 ⁢ a + z ) + 1 3 ⁢ ( z 2 ⁢ a + z ) 3 + 1 5 ⁢ ( z 2 ⁢ a + z ) 5 + ⋯ ) , 𝑧 𝑎 𝑎 2 𝑧 2 𝑎 𝑧 1 3 superscript 𝑧 2 𝑎 𝑧 3 1 5 superscript 𝑧 2 𝑎 𝑧 5 ⋯ {\displaystyle{\displaystyle\ln\left(z+a\right)=\ln a+2\left(\left(\frac{z}{2a% +z}\right)+\frac{1}{3}\left(\frac{z}{2a+z}\right)^{3}+\frac{1}{5}\left(\frac{z% }{2a+z}\right)^{5}+\cdots\right),}}
    0 references
    DLMF id
    DLMF:4.6.E6
    0 references
    constraint
    ℜ ⁡ z ≥ - a 𝑧 𝑎 {\displaystyle{\displaystyle\Re z\geq-a}}
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    ℜ ⁡ z ≥ - a 𝑧 𝑎 {\displaystyle{\displaystyle\Re z\geq-a}}
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    z ≠ - a 𝑧 𝑎 {\displaystyle{\displaystyle z\neq-a}}
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    Symbols used
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aedec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1abdec
    0 references
     
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