The inverse hyperbolic cosecant csch^(-1) z, sometimes called the area hyperbolic cosecant and sometimes denoted cosech^(-1) z or arccsch z, is the multivalued function that is the inverse function of the hyperbolic cosecant. The variants Arccsch z and Arcsch z are sometimes used to refer to explicit principal values. Worse yet, the notation arccsch z is sometimes used for the principal value, with Arccsch z being used for the multivalued function. Note that in the notation csch^(-1) z, csch z is the hyperbolic cosecant and the superscript -1 denotes an inverse function, not the multiplicative inverse.
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