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

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