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

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2003-08-21