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

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2003-08-21