To rigorously define inverse hyperbolic cosine, we need to make a branch cut. We cannot define arccosh as an analytic function over the entire complex plane. But if we remove (−∞, 1], we can. We define arccosh(x) for real x 1 to be the positive real number y such that cosh(y) = x, and define it for the rest of the complex plane (with our branch cut (−∞, 1] removed) by analytic continuation.
Дмитрий ПесковПресс-секретарь президента России
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