DLMF:4.37.E24 (Q1943)

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Language	Label	Description	Also known as
English	DLMF:4.37.E24	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\operatorname{arctanh}z=\tfrac{1}{2}\ln\left(\frac% {1+z}{1-z}\right),}}

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DLMF:4.37.E24

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{\displaystyle{\displaystyle z\in\mathbb{C}\setminus(-\infty,-1]\cup[1,\infty)}}

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Defining formula

{\displaystyle{\displaystyle[\NVar{a},\NVar{b})}}

introduction.Sx4.p2.t1.r1.m4aadec

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Defining formula

{\displaystyle{\displaystyle\mathbb{C}}}

introduction.Sx4.p1.t1.r1.m2acdec

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Defining formula

{\displaystyle{\displaystyle\in}}

introduction.Sx4.p1.t1.r10.m2agdec

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Defining formula

{\displaystyle{\displaystyle\operatorname{arctanh}\NVar{z}}}

C4.S37.SS2.p1.m10acdec

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principal branch of logarithm function

Defining formula

{\displaystyle{\displaystyle\ln\NVar{z}}}

C4.S2.E2.m2ahdec

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Defining formula

{\displaystyle{\displaystyle(\NVar{a},\NVar{b}]}}

introduction.Sx4.p2.t1.r1.m3acdec

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Defining formula

{\displaystyle{\displaystyle\setminus}}

introduction.Sx4.p2.t1.r19.m2acdec

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Sitelinks

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