D[ArcCosh[z], {z, n}] == (-(Sqrt[z - 1]/Sqrt[1 - z])) 2^(n - 1) Sqrt[Pi] z^(1 - n) HypergeometricPFQRegularized[{1/2, 1/2, 1}, {1 - n/2, (3 - n)/2}, z^2] /; Element[n, Integers] && n >= 0

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2001-10-29