DLMF:4.37.E18 (Q1937): Difference between revisions

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Property / constraint
 

y ( - , - 1 ] 𝑦 1 {\displaystyle{\displaystyle y\in(-\infty,-1]}}

y\in(-\infty,-1]
Property / constraint: y ( - , - 1 ] 𝑦 1 {\displaystyle{\displaystyle y\in(-\infty,-1]}} / rank
 
Normal rank

Revision as of 16:03, 30 December 2019

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DLMF:4.37.E18
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    Statements

    arcsinh ( i y ) = - 1 2 π i ± ln ( ( y 2 - 1 ) 1 / 2 - y ) , hyperbolic-inverse-sine 𝑖 𝑦 plus-or-minus 1 2 𝜋 𝑖 superscript superscript 𝑦 2 1 1 2 𝑦 {\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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    y ( - , - 1 ] 𝑦 1 {\displaystyle{\displaystyle y\in(-\infty,-1]}}
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