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Formula:1627

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Digital Library of Mathematical Functions ID 4.6.E4

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),}}


Constraint(s)

ℜ ⁡ z ≥ 0 𝑧 0 {\displaystyle{\displaystyle\Re z\geq 0}}
ℜ ⁡ z ≥ 0 𝑧 0 {\displaystyle{\displaystyle\Re z\geq 0}}
z ≠ 0 𝑧 0 {\displaystyle{\displaystyle z\neq 0}}

Symbols List

  • ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}} : principal branch of logarithm function
  • ℜ ⁡ absent {\displaystyle{\displaystyle\Re}} : real part
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  •  Edit this on Wikidata

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This page was last edited on 3 March 2024, at 01:41.
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