DLMF:4.37.E17 (Q1936)

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Language	Label	Description	Also known as
English	DLMF:4.37.E17	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\operatorname{arcsinh}\left(iy\right)=\tfrac{1}{2}% \pi i\pm\ln\left((y^{2}-1)^{1/2}+y\right),}}

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DLMF:4.37.E17

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{\displaystyle{\displaystyle y\in[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.m2abdec

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Defining formula

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

introduction.Sx4.p2.t1.r1.m4adec

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Defining formula

{\displaystyle{\displaystyle\in}}

introduction.Sx4.p1.t1.r10.m2aadec

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Defining formula

{\displaystyle{\displaystyle\operatorname{arcsinh}\NVar{z}}}

C4.S37.SS2.p1.m8addec

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Defining formula

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

C1.S9.E1.m2acdec

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principal branch of logarithm function

Defining formula

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

C4.S2.E2.m2aadec

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Defining formula

{\displaystyle{\displaystyle y}}

C4.S1.XMD7.m1dec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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