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

**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.

© 1996-9

1999-05-25