DLMF:4.6.E4 (Q1573): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
test:

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

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1aadec

Revision as of 17:08, 1 January 2020

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English
DLMF:4.6.E4
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    Statements

    test
    ln ⁡ z = 2 ⁢ ( ( z - 1 z + 1 ) + 1 3 ⁢ ( z - 1 z + 1 ) 3 + 1 5 ⁢ ( z - 1 z + 1 ) 5 + ⋯ ) , 𝑧 2 𝑧 1 𝑧 1 1 3 superscript 𝑧 1 𝑧 1 3 1 5 superscript 𝑧 1 𝑧 1 5 ⋯ {\displaystyle{\displaystyle\ln z=2\left(\left(\frac{z-1}{z+1}\right)+\frac{1}% {3}\left(\frac{z-1}{z+1}\right)^{3}+\frac{1}{5}\left(\frac{z-1}{z+1}\right)^{5% }+\cdots\right),}}
    0 references
    DLMF id
    DLMF:4.6.E4
    0 references
    constraint
    ℜ ⁡ z ≥ 0 𝑧 0 {\displaystyle{\displaystyle\Re z\geq 0}}
    0 references
    ℜ ⁡ z ≥ 0 𝑧 0 {\displaystyle{\displaystyle\Re z\geq 0}}
    0 references
    z ≠ 0 𝑧 0 {\displaystyle{\displaystyle z\neq 0}}
    0 references
    Symbols used
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
    0 references
    Q10811
    test
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aadec
    0 references
     
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