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Article 11 — Appendix A.13artanh or arth — archyperbolic tangent functionCategory. Mathematics. Abstract. Archyperbolic tangent: definition, graph, properties and identities. References. This article is a part of scientific calculator LiL, scientific calculator LiX, scientific calculator LiLc and scientific calculator LiXc products. 1. DefinitionArchyperbolic tangent is inverse of hyperbolic tangent function. With the help of natural logarithm it can be represented as: artanhx ≡ ln[(1 + x) /(1 − x)] /22. GraphArchyperbolic tangent is antisymmetric function defined in the range (−1, 1), points x = ±1 are singular ones. Its graph is depicted below — fig. 1. Fig. 1. Graph of the archyperbolic tangent function y = artanhx.Function codomain is entire real axis. 3. IdentitiesProperty of antisymmetry: artanh−x = −artanhxReciprocal argument: artanh(1/x) = arcothxSum and difference: artanhx + artanhy = artanh[(x + y) /(1 + xy)]artanhx − artanhy = artanh[(x − y) /(1 − xy)] 4. SupportArchyperbolic tangent function artanh or arth is supported in: Archyperbolic tangent function of the complex argument artanh or arth is supported in:
5. How to useTo calculate archyperbolic tangent of the number:
To calculate archyperbolic tangent of the current result:
To calculate archyperbolic tangent of the number x in memory:



