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

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2003-08-21