ArcCsch[z] == (Pi/4) (I Sqrt[z/(z + I Sqrt[2])] Sqrt[(z + I Sqrt[2])/z] Sqrt[I/z] Sqrt[(-I) z] - I Sqrt[z/(z - I Sqrt[2])] Sqrt[(z - I Sqrt[2])/z] Sqrt[-(I/z)] Sqrt[I z] - (Sqrt[(1 + z^2)/z^4] z)/Sqrt[-((z^2 + 1)/z^2)] - Sqrt[-(1/z^2)] z) - ((Sqrt[-1 - I z] Sqrt[-1 + I z] Sqrt[-z])/(2 Sqrt[z] Sqrt[1 + z^2])) ArcCsc[z^2/(2 Sqrt[-1 - z^2])]

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</mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arccsch /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> 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2003-08-21