The inverse hyperbolic sine sinh^(-1) z, sometimes called the area hyperbolic sine is the multivalued function that is the inverse function of the hyperbolic sine. The variants Arcsinh z or Arsinh z are sometimes used to refer to explicit principal values of the inverse hyperbolic sine, although this distinction is not always made. Worse yet, the notation arcsinh z is sometimes used for the principal value, with Arcsinh z being used for the multivalued function. The notations arcsinh z and Arsh z (Gradshteyn and Ryzhik 2000, p. xxx) are sometimes also used. Note that in the notation sinh^(-1) z, sinh z is the hyperbolic sine and the superscript -1 denotes an inverse function, not the multiplicative inverse.
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