hyperbolic function

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun 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.
• noun The hyperbolic sine, defined by the equation sinh x = ¹/₂ (e^x − e^−x).
• noun The hyperbolic cosine, defined by the equation cosh x = ¹/₂ (e^x + e^−x).
• noun The hyperbolic tangent, defined by the equation tanh x = sinh x/cosh x.
• noun The hyperbolic cotangent, defined by the equation coth x = cosh x/sinh x.
• noun The hyperbolic secant, defined by the equation sech x = 1/cosh x.
• noun The hyperbolic cosecant, defined by the equation csch x = 1/sinh x.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun 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.