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Formula:2377

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Digital Library of Mathematical Functions ID 4.37.E29

w = Arcsinh ⁡ z = ( - 1 ) k ⁢ arcsinh ⁡ z + k ⁢ π ⁢ i , 𝑤 multivalued-hyperbolic-inverse-sine 𝑧 superscript 1 𝑘 hyperbolic-inverse-sine 𝑧 𝑘 𝜋 𝑖 {\displaystyle{\displaystyle w=\operatorname{Arcsinh}z=(-1)^{k}\operatorname{% arcsinh}z+k\pi i,}}


Constraint(s)

Symbols List

  • π {\displaystyle{\displaystyle\pi}} : the ratio of the circumference of a circle to its diameter
  • arcsinh ⁡ z hyperbolic-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{arcsinh}\NVar{z}}} :
  • i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}} : imaginary unit
  • Arcsinh ⁡ z multivalued-hyperbolic-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{Arcsinh}\NVar{z}}} : general inverse hyperbolic sine function
  • k 𝑘 {\displaystyle{\displaystyle k}} : integer
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  •  Edit this on Wikidata

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