DLMF:4.23.E26 (Q1778): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:4.23.E26	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\operatorname{arctan}z=\frac{i}{2}\ln\left(\frac{i% +z}{i-z}\right),}}

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DLMF:4.23.E26

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{\displaystyle{\displaystyle z/i\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.m4abdec

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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\mathrm{i}}}

C1.S9.E1.m2akdec

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Defining formula

{\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}

C4.S23.SS2.p1.m7addec

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principal branch of logarithm function

Defining formula

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

C4.S2.E2.m2agdec

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Defining formula

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

introduction.Sx4.p2.t1.r1.m3abdec

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Defining formula

{\displaystyle{\displaystyle\setminus}}

introduction.Sx4.p2.t1.r19.m2acdec

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Defining formula

{\displaystyle{\displaystyle\cup}}

introduction.Sx4.p1.t1.r28.m2acdec

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Defining formula

{\displaystyle{\displaystyle z}}

C4.S1.XMD8.m1vdec

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Sitelinks

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