hyperbolic function


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Related to hyperbolic function: Inverse hyperbolic function

hyperbolic function

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:
a. The hyperbolic sine, defined by the equation sinh x = 1/2 (ex - e-x).
b. The hyperbolic cosine, defined by the equation cosh x = 1/2 (ex + e-x).
c. The hyperbolic tangent, defined by the equation tanh x = sinh x/cosh x.
d. The hyperbolic cotangent, defined by the equation coth x = cosh x/sinh x.
e. The hyperbolic secant, defined by the equation sech x = 1/cosh x.
f. The hyperbolic cosecant, defined by the equation csch x = 1/sinh x.

hyperbolic function

n
(Mathematics) any of a group of functions of an angle expressed as a relationship between the distances of a point on a hyperbola to the origin and to the coordinate axes. The group includes sinh (hyperbolic sine), cosh (hyperbolic cosine), tanh (hyperbolic tangent), sech (hyperbolic secant), cosech (hyperbolic cosecant), and coth (hyperbolic cotangent)

hy′perbol′ic func′tion


n.
a function of an angle expressed as a relationship between the distances from a point on a hyperbola to the origin and to the coordinate axes, as hyperbolic sine or hyperbolic cosine.
[1885–90]
References in periodicals archive ?
The first was fitting the amounts/percents across the different delays to a hyperbolic function (e.
This function is frequently included with the hyperbolic function as a point of comparison.
In this case, the GWBASIC language program takes in consideration only five distinct functions like: the exponential function, 1nd and 2nd degree polynomial function, power function and hyperbolic function.
Accurate quantitative predictions for this choice situation can be made by assuming that a reinforcer's value decreases according to a hyperbolic function with increasing delay, as specified in Equations 1 and 2.
However, even in the literature, which uses relatively sophisticated statistical techniques to gauge how well a hyperbolic function fits the data, unusual cases make the estimation results less convincing.
This generates the characteristic hyperbolic function that is typically associated with reinforcement bars.
One disadvantage of the hyperbolic function is that age-price functions estimated from a hyperbolic function (or alternatively, hyperbolic functions estimated from an age-price function) require an assumption to be made about a real discount rate.
Roy first gives readers a background in Riemann's zeta function and von Magoldt's work on the xi functions, then turns to theory, explaining basic arithmetic functions, Argand diagrams, Euler identities, powers and logarithms, the hyperbolic function, standard integration with complex numbers, and line and contour integration.
Perhaps the most popular analysis method is to fit the indifference points at each delay or probability with a hyperbolic function (Mazur, 1987).
Findings from behavioral economic studies suggest that the discount rate for values in a future period is not an exponential function of delay, as the standard discounted utility model implies, but is better described as a hyperbolic function, in which the rate of discounting decreases with the passage of time (Ainslie, 1992, 2001; Chong & Herrnstein, 1967).