DLMF:4.23.E23 (Q1775)

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Language	Label	Description	Also known as
English	DLMF:4.23.E23	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\operatorname{arccos}z=-2i\ln\left(\left(\frac{1+z% }{2}\right)^{1/2}+i\left(\frac{1-z}{2}\right)^{1/2}\right),}}

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DLMF:4.23.E23

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

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Defining formula

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

introduction.Sx4.p1.t1.r1.m2abdec

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Defining formula

{\displaystyle{\displaystyle\in}}

introduction.Sx4.p1.t1.r10.m2addec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2ahdec

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Defining formula

{\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}

C4.S23.SS2.p1.m6aedec

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principal branch of logarithm function

Defining formula

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

C4.S2.E2.m2addec

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Defining formula

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

introduction.Sx4.p1.t1.r29.m6abdec

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Defining formula

{\displaystyle{\displaystyle\setminus}}

introduction.Sx4.p2.t1.r19.m2abdec

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Defining formula

{\displaystyle{\displaystyle\cup}}

introduction.Sx4.p1.t1.r28.m2abdec

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Defining formula

{\displaystyle{\displaystyle z}}

C4.S1.XMD8.m1udec

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