Because the exponential purpose is usually described for almost any sophisticated argument, we will increase the definitions with the hyperbolic capabilities also to advanced arguments. The functions sinh z and cosh z are then holomorphic.
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is the base of your natural logarithm Log. Cosh mechanically evaluates to exact values when its argument would be the (purely natural) logarithm of a rational variety.
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The inverse hyperbolic capabilities are several-valued and as in the case of inverse trigonometric features we limit ourselves to principal values for which they are often regarded as one-valued.