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.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

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)
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

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]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
References in periodicals archive ?
The hyperbolic-type control schemes work as follows: for large errors [[??].sub.i], the hyperbolic function cosh [mathematical expression not reproducible] returns a bounded control output avoiding input saturation in the servo amplifier; when the errors [[??].sub.i] are small, that hyperbolic function is approximately linear; then it works like proportional controller.
Hyperbolic function solution, trigonometric function solution, and rational solution with general parameters are obtained.
Caption: FIGURE 7: Prediction model for the settlement of the road shoulder: (a) hyperbolic function; (b) logarithmic function; (c) power function; (d) exponential function.
However, Mazur's hyperbolic function and the AUC are arguably the two most commonly used measures of DD.
The slow upswing action potential in the Izhikevich model and AdEx model is improved by the hyperbolic function (Table 1).
The Linear Hyperbolic function (LHF) can be used to describe milk yield and the percentages of fat and protein curves between different ages and calving seasons.
of Name of Type of equation empirical model mathematical model 1 Reeve (1957) Hyperbolic function 2 Dieleman (1963) Exponential function 3 Leffelaar & Shama (1977) Hyperbolic function 4 Hoffman (1980) Hyperbolic function 5 Pazira & Kawachi (1998) Hyperbolic function 6 Verma and Gupta (1989) Power function 7 Power function 8 Pazira & Keshavarz (1998) Power function 9 Rajabzadeh (2009) Exponential function 10 Asadi (2011) Logarithmic function 11 Asadi (2012) Logarithmic function 12 Mohammadzadeh (2013) Power function No.
Consequently, as before, when [[lambda].sup.2] - 4[mu] > 0, we obtain the hyperbolic function solutions:
The tangent hyperbolic function can be arranged in a vector in the following way:
Let function [[eta].sub.1] be a hyperbolic function of time t; that is, [[eta].sub.1] = cosh([[OMEGA].sub.3]t), and then we have