ArcCos[(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) + ((4 Sqrt[1 - 1/z])/Sqrt[1/z - 1]) ArcSech[z])

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2003-08-21