The earliest and most widely adopted symbols use the prefix arc- (that is: arcsinh, arccosh, arctanh, arcsech, arccsch, arccoth), by analogy with the inverse circular functions (arcsin, etc.).

6 天之前 · The inverse hyperbolic sine (Beyer 1987, p. 181; Zwillinger 1995, p. 481), sometimes called the area hyperbolic sine (Harris and Stocker 1998, p. 264) is the multivalued function that is the inverse function of the hyperbolic sine.

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2024年11月4日 · Inverse hyperbolic functions are the inverse functions of the hyperbolic sine, cosine, tangent, and other hyperbolic functions. They are used to solve equations involving hyperbolic functions and are expressed in terms of logarithmic formulas. The three basic inverse hyperbolic functions are:

ArcSinh [z] gives the inverse hyperbolic sine sinh -1 (z) of the complex number z.

The hyperbolic sine function, \sinh x, is one-to-one, and therefore has a well-defined inverse, \sinh^ {-1} x, shown in blue in the figure. In order to invert the hyperbolic cosine function, however, we need (as with square root) to restrict its domain. By convention, \cosh^ {-1} x is taken to mean the positive number y such that x=\cosh y.

Inverse hyperbolic sineArcSinh [<i>z</i>] (2442 formulas)

It's because arcsin gives the arc length on the unit circle for a given y-coordinate, whereas arsinh gives an area enclosed by a hyperbola and two rays from the origin for a given y-coordinate. The red shaded area below is equal to arsinh (a), where a is the length of the blue line segment. Relation between arsinh and areas for a hyperbola.

2025年4月1日 · See Inverse Hyperbolic Sine Related Wolfram sites http://functions.wolfram.com/ElementaryFunctions/ArcSinh/

The calculator will find the inverse hyperbolic sine of the given value. The inverse hyperbolic sine y=\sinh^ {-1} (x) y = sinh−1(x) or y=\operatorname {asinh} (x) y = asinh(x) or y=\operatorname {arcsinh} (x) y = arcsinh(x) is such a function that \sinh (y)=x sinh(y) = x.