## TAYLOR SERIES ARCCOSH

Many functions, such as diff , int , taylor , and rewrite , can handle expressions containing acosh. Inverse hyperbolic cosecant aka area hyperbolic cosecant Latin: Hyperbolic functions and their inverses occur in many linear differential equations , for example the equation defining a catenary , of some cubic equations , in calculations of angles and distances in hyperbolic geometry and of Laplace’s equation in Cartesian coordinates. Based on your location, we recommend that you select: Quadratic and Cubic Equations”. Retrieved 3 November For real , it satisfies.

In these formulas, the argument of the logarithm is real if and only if z is real. Inverse hyperbolic functions in the complex z-plane: By using this site, you agree to the Terms of Use and Privacy Policy. Handle Expressions Containing Inverse Hyperbolic Cosine Function Many functions, such as diff , int , taylor , and rewrite , can handle expressions containing acosh. Inverse Hyperbolic Cosine Function for Numeric and Symbolic Arguments Depending on its arguments, acosh returns floating-point or exact symbolic results. Simplify the result by using simplify. The Art of Scientific Computing 2nd ed.

If the argument of the logarithm is real, then z is a taypor real number, and this implies that the argument of the logarithm is positive. In other words, the above defined branch cuts are minimal.

### Symbolic inverse hyperbolic cosine function – MATLAB acosh

Inverse hyperbolic secant aka area hyperbolic secant Latin: For all inverse hyperbolic functions but the inverse hyperbolic cotangent and the inverse hyperbolic cosecant, the domain of the real function is connected. Find the indefinite integral of the inverse hyperbolic cosine function. BronshteinKonstantin A.

Handbook of Mathematics and Computational Science. This defines a single valued analytic function, which is defined everywhere except for non-positive real values of the variables where the two square roots have a zero real part. Based on your location, we recommend that you select: Many functions, such as diffinttaylorand rewritecan handle expressions containing acosh.

When possible, it is better to define the principal value directly, without referring to analytic continuation.

As functions of a complex variableinverse hyperbolic functions are multivalued functions that are analytic except at a finite number of points. This gives the principal value. The name area refers to the fact that the geometric definition of the functions is the area of certain hyperbolic sectors Inverse hyperbolic cosecant aka area hyperbolic cosecant Latin: Input Arguments collapse all X — Input symbolic number symbolic variable symbolic expression symbolic function symbolic vector symbolic matrix.

## Inverse hyperbolic functions

Click the button below to return to the English version of the page. For such a function, it is common to define a principal valuewhich is a single valued analytic function which coincides with one specific branch of the multivalued function over a domain consisting of the complex plane in which a finite number of arcs usually half lines or line segments have been removed.

The latter are misnomers, since the prefix arc is the abbreviation for arcuswhile the prefix ar stands for area. Simplify the result by using simplify. By using this site, you agree to the Arcccosh of Use and Privacy Policy. As the hyperbolic functions are rational functions of e x whose numerator and denominator are of degree at most two, these functions may be solved in terms of e xby using the quadratic formula ; then, taking the natural logarithm gives the following expressions for the inverse hyperbolic functions.

The inverse hyperbolic cosine is a multivalued function and hence requires a branch cut in the complex planewhich the Wolfram Language ‘s convention places at the line segment.

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Use vpa to approximate symbolic results with floating-point numbers:. Inverse Hyperbolic Cosine Function for Numeric and Symbolic Arguments Depending on its arguments, acosh returns floating-point or exact symbolic results. If the argument of the logarithm is real and negative, then z is also real and negative. In seris following graphical representation of the principal values of the inverse hyperbolic functions, the branch cuts appear as discontinuities of the color.

The variants and Harris and Stockerp. Retrieved 3 November In these formulas, the argument of the logarithm is real if and only if z is real. Trial Software Product Updates.

It is defined when the arguments of the logarithm and the square root are not non-positive real numbers. Mathematics for Physicists and Engineers: Select the China site in Chinese or English for best site performance.

MathWorks does not warrant, and disclaims all liability for, the accuracy, suitability, or fitness for purpose of the translation. See Also acoth acsch asech asinh atanh cosh coth csch sech sinh tanh.

Quadratic and Cubic Equations”. In mathematicsthe inverse hyperbolic functions are the inverse functions of the hyperbolic functions.

Plot the inverse hyperbolic cosine function on the interval from 1 to For all inverse hyperbolic functions, the principal value may be defined in terms of principal values of the square root and the logarithm function. The area functions are the inverse functions of the hyperbolic functions, i. Springer-Verlagwrccosh ed. The automated translation of this page is provided by a general purpose third party translator tool.

Note that in the notationis the hyperbolic cosine and the superscript denotes an inverse functionnot the multiplicative inverse. If arcvosh argument of the logarithm is real, then it is positive.