hyperbolic function

(redirected from Hyperbolic curve)

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 ?
When two branches of hyperbolic curve are intersected with some boundary surface, ambiguity of connection means comes up.
We have to go up the hyperbolic curve and have people's candidates everywhere in the city from Bhayandar to Colaba," asserts Vora.
production data for Alaska are typically reported to the EIA before the interim estimate is made); (b) first purchase data reported on Form EIA-182, "Domestic Crude Oil First Purchase Report;" (c) exponential or hyperbolic curve fitted projections based on recent State data; or (d) constant level projections based on the average production rate during a recent time period.
How useful is a hyperbolic curve for quotients in these circumstances?
We modified the contour by blending a hyperbolic curve into the superelliptical curve and generated a dumbbell-like contour.
Parallel's current performance "type curve" anticipates the typical horizontal Wolfcamp well will exhibit an initial gross gas rate of approximately 2,100 Mcf of gas per day and a hyperbolic curve shape which yields approximately 2 BCF of gross gas reserves over a 17-year period.
Total dollar volume processed by the platform has followed a classic hyperbolic curve since its inception in 1998 -- slow at the beginning, trending sharply up at the present.