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Exponential, logarithmic and hyperbolic functions and an introduction to complex functions
Published in Alan Jeffrey, Mathematics, 2004
It is often convenient to express the inverse hyperbolic functions in terms of the natural logarithmic function. To show how this may be accomplished, we derive the expression arcsinh(xa)=ln[xa+a2+x2|a|],
Introduction and Review
Published in Russell L. Herman, A Course in Mathematical Methods for Physicists, 2013
There also exist inverse hyperbolic functions and these can be written in terms of logarithms. As with the inverse trigonometric functions, we begin with the definition () y=sinh−1x⇔x= sinh y.
Differentiation of inverse trigonometric and hyperbolic functions
Published in John Bird, Higher Engineering Mathematics, 2017
Inverse hyperbolic functions are denoted by prefixing the function with ‘ar’ or, more commonly, by using the −1 notation. For example, if y = sinhx, then x = arsinh y or x = sinh−1 y. Similarly, if y = sechx, then x = arsech y or x = sech−1y, and so on. In this chapter the −1 notation will be used. A sketch of each of the inverse hyperbolic functions is shown in Fig. 38.2.
An asinh-type regulator for robot manipulators with global asymptotic stability
Published in Automatika, 2020
Fernando Reyes-Cortes, Basil M. Al-Hadithi
Within the group of inverse hyperbolic functions, in addition to the asinh function, there are also the atanh and acosh functions. However, the acosh function is defined only (at least where real vectors are concerned), for . Its behavior is only in the first quadrant, so it does not return negative values, then this function could not be evaluated as a control scheme.