Article 11 — Appendix A.13

artanh or arth — arc-hyperbolic tangent function

Category. Mathematics.

Abstract. Arc-hyperbolic tangent: definition, plot, properties and identities.

Reference. This article is a part of Librow scientific formula calculator project.

1. Definition

Arc-hyperbolic tangent is inverse of hyperbolic tangent function. With the help of natural logarithm it can be represented as:

2. Plot

Arc-hyperbolic tangent is antisymmetric function defined in the range (−1, 1), points x = ±1 are singular ones. Its plot is depicted below — fig. 1.

Function codomain is entire real axis.

3. Identities

Property of antisymmetry:

Reciprocal argument:

Sum and difference:

4. Support

Arc-hyperbolic tangent function artanh or arth of the real argument is supported by free version of the Librow calculator.

Arc-hyperbolic tangent function artanh or arth of the complex argument is supported by professional version of the Librow calculator.

5. How to use

To calculate arc-hyperbolic tangent of the number:

artanh(-.5);

To calculate arc-hyperbolic tangent of the current result:

artanh(rslt);

To calculate arc-hyperbolic tangent of the number x in memory:

artanh(mem[x]);