Definitions

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • abbr. The inverse hyberbolic tangent function

Etymologies

arc- +‎ tanh (Wiktionary)

Examples

  • HYPERBOLIC ARCTANGENT Figure 4-9 is a graph of the function y ¼ arctanh x (or y ¼ tanhÀ1 x).

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  • In for - mulas and equations, they are abbreviated arcsinh or sinhÀ1, arccosh or coshÀ1, arctanh or tanhÀ1, arccsch or cschÀ1, arcsech or sechÀ1, and arccoth or cothÀ1 respectively.

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  • CHAPTER 4 Hyperbolic Functions 65 arcsinh x ¼ ln ½x þ ðx2 þ 1Þ1 = 2 Š arccosh x ¼ ln ½x þ ðx2 À 1Þ1 = 2 Š arctanh x ¼ 0: 5 ln ½ð1 þ xÞ = ð1 À xÞŠ arccsch x ¼ ln ½xÀ1 þ ðxÀ2 þ 1Þ1 = 2 Š arcsech x ¼ ln ½xÀ1 þ ðxÀ2 À 1Þ1 = 2 Š arccoth x ¼ 0: 5 ln ½ðx þ 1Þ = ðx À 1ÞŠ In these expressions, the values 0.5 represent exactly 1 = 2.

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  • {arcsinh, arccosh, arctanh} (float | complex): float | complex

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