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

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2003-08-21