DLMF:4.6.E4 (Q1573)

From DRMF
Revision as of 18:08, 1 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:4.6.E4
No description defined

    Statements

    Defining formula
    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
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aadec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1cdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q1573&oldid=26737"