hyperbolic function

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Related to Hyperbolic cosine: Hyperbolic sine, Inverse hyperbolic cosine

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 register-transfer level (RTL) schematic of hyperbolic cosine function given by (9) is not shown while the RTL schematic of proposed autonomous jerk oscillator is shown in Figure 8.
Next, we formulate the following properties for Riemann-Liouville derivatives of the hyperbolic sine and hyperbolic cosine functions.
Clearly one can replace the hyperbolic sine in the preceding discussion by the hyperbolic cosine in (43) to obtain the third solution [[PHI].sup.(3)]([tau], [rho]) in (10).