DLMF:4.23.E27 (Q1779)

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Language	Label	Description	Also known as
English	DLMF:4.23.E27	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\operatorname{arctan}\left(iy\right)=\pm\frac{1}{2% }\pi+\frac{i}{2}\ln\left(\frac{y+1}{y-1}\right),}}

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DLMF:4.23.E27

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{\displaystyle{\displaystyle y\in(-\infty,-1)\cup(1,\infty)}}

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aidec

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Defining formula

{\displaystyle{\displaystyle\in}}

introduction.Sx4.p1.t1.r10.m2ahdec

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Defining formula

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

C1.S9.E1.m2aldec

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Defining formula

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

C4.S23.SS2.p1.m7aedec

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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.p1.t1.r29.m6acdec

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Sitelinks

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