ArcCosh[(2 Sqrt[z^2 - 1])/z^2] == (Sqrt[(2 Sqrt[z^2 - 1])/z^2 - 1]/Sqrt[1 - (2 Sqrt[z^2 - 1])/z^2]) (Pi/2 + ((z^3 Sqrt[(1 - z^2)/z^4] Sqrt[-2 + z^2] Sqrt[-1 + z^2] Sqrt[1/z] Sqrt[-((1 + z)/z)])/(2 Sqrt[1 - z] (z + 1) Sqrt[-2 + 3 z^2 - z^4])) (Pi ((Sqrt[(1 - z^2)/z^2] Sqrt[(1 - z^2)/z^4] z^3)/(1 - z^2) + Sqrt[1/z^2] z + Sqrt[1 - 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 Pi + 4 ArcSec[z]))

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2 </mn> </msqrt> </mrow> </mfrac> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> sec </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arccosh /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 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2003-08-21