## Hyperbolic Tangent

By way of analogy with the usual Tangent

the hyperbolic tangent is defined as

where is the Hyperbolic Sine and is the Hyperbolic Cosine. The hyperbolic tangent can be written using a Continued Fraction as

See also Bernoulli Number, Catenary, Correlation Coefficient--Gaussian Bivariate Distribution, Fibonacci Hyperbolic Tangent, Fisher's z'-Transformation, Hyperbolic Cotangent, Lorentz Group, Mercator Projection, Oblate Spheroidal Coordinates, Pseudosphere, Surface of Revolution, Tangent, Tractrix, Tractroid

References

Abramowitz, M. and Stegun, C. A. (Eds.). Hyperbolic Functions.'' §4.5 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 83-86, 1972.

Spanier, J. and Oldham, K. B. The Hyperbolic Tangent and Cotangent Functions.'' Ch. 30 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 279-284, 1987.