hyperbolic function

American Heritage® Dictionary of the English Language, Fourth Edition

1. n. Any of a set of six functions related, for a real or complex variable x, to the hyperbola in a manner analogous to the relationship of the trigonometric functions to a circle, including:
2. n. The hyperbolic sine, defined by the equation sinh x = ¹/₂ (e^x - e^-x).
3. n. The hyperbolic cosine, defined by the equation cosh x = ¹/₂ (e^x + e^-x).
4. n. The hyperbolic tangent, defined by the equation tanh x = sinh x/cosh x.
5. n. The hyperbolic cotangent, defined by the equation coth x = cosh x/sinh x.
6. n. The hyperbolic secant, defined by the equation sech x = 1/cosh x.
7. n. The hyperbolic cosecant, defined by the equation csch x = 1/sinh x.

Wiktionary

1. n. mathematics A function that is derived from some arithmetic operations on the exponential function with base e and the inverse function, and was named after the corresponding similar trigonometric function.