
	Where results make sense

Topic: Hyperbolic function

Related Topics

Airy function

List of functions

List of coshes

Hyperbolic angle

Bessel differential equation

Table of derivatives

Error function

Inverse function

List of integrals of arc functions

Gamma function

Gudermannian function

Trigonometric function

Maclaurin series

Beta function

Exponential function

	Hyperbolic function - Wikipedia, the free encyclopedia
		In mathematics, the hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.
		Hyperbolic functions are also useful because they occur in the solutions of some simple linear differential equations, notably that defining the shape of a hanging cable, the catenary.
		The inverses of the hyperbolic functions are the area hyperbolic functions.
	en.wikipedia.org /wiki/Hyperbolic_function (707 words)

	Design and Analysis of Queue Control Functions for Explicit Rate Switch Schemes (Site not responding. Last check: 2007-09-17)
		The curve used in the control function in the underload region is called the ``a-curve'' and the one used in the overload region is called the ``b-curve''.
		The behavior of the system is the same as in the case of the hyperbolic function for underload and the steady state range of queue lengths.
		, the queue decreases hyperbolically (inverse function of f(Q)'s a-curve).
	www.cse.wustl.edu /~jain/papers/ftp/qctrl_bv (3518 words)

	Karl's Calculus Tutor - 11.5 Hyperbolic Substitution
		If hyperbolic substitution is not part of your curriculum, then skip ahead (unless you're curious) to Partial Fractions, and don't worry, we will cover the methods to integrate the functions that are covered here later on.
		The integrands that the hyperbolic functions address are all analogs of the ones that the trig functions were able to address.
		Since we were able to construct the hyperbolic functions from exponentials, it shouldn't surprise you that we can construct their inverses from logs.
	www.karlscalculus.org /hyper.html (2129 words)

	[No title] (Site not responding. Last check: 2007-09-17)
		The function cosh x is always positive, symmetric with respect to the y-axis and satisfies cosh 0 = 1, the function sinh x is symmetric with respect to the origin and hence sinh 0 = 0.
		The k2,obs data were fitted empirically to a hyperbolic function to estimate k2 (Equation3) or k3 (Equation4) to be 110 s1 for the reaction with 15-HPETE and 25s1 for the reaction with EtOOH (Fig.
		Validation of the use of a hyperbolic function for estimation of k2 in the first mechanism (Equation3) is detailed below.
	www.lycoszone.com /info/hyperbolic-function.html (392 words)

	CLHS: Function SINH, COSH, TANH, ASINH...
		These functions compute the hyperbolic sine, cosine, tangent, arc sine, arc cosine, and arc tangent functions, which are mathematically defined for an argument x as given in the next figure.
		The branch cut for the inverse hyperbolic sine function is in two pieces: one along the positive imaginary axis above i (inclusive), continuous with quadrant I, and one along the negative imaginary axis below -i (inclusive), continuous with quadrant III.
		Thus the range of the inverse hyperbolic tangent function is identical to that of the inverse hyperbolic sine function with the points -i/2 and i/2 excluded.
	www.lisp.org /HyperSpec/Body/fun_sinhcm_co_coshcm_atanh.html (460 words)

	ANSI and GNU Common Lisp Document - sinh
		These functions compute the hyperbolic sine, cosine, tangent, arc sine, arc cosine, and arc tangent functions, which are mathematically defined for an argument x as given in Figure 12--15.
		The branch cut for the inverse hyperbolic tangent function is in two pieces: one along the negative real axis to the left of -1 (inclusive), continuous with quadrant III, and one along the positive real axis to the right of~1 (inclusive), continuous with quadrant I. The points -1 and~1 are excluded from the domain.
		Thus the range of the inverse hyperbolic tangent function is identical to that of the inverse hyperbolic sine function with the points -\pi i/2 and~\pi i/2 excluded.
	www.cs.queensu.ca /software_docs/gnudev/gcl-ansi/gcl_767.html (523 words)

	Function Grapher two variable, AMIR's
		In addition to algebraic functions such as linear, quadratic and other polynomial and rational functions, you can use any of these predefined functions in your expressions, including power functions, logarithmic and exponential functions, trigonometric functions and their inverses, and hyperbolic functions and their inverses.
		The graph of a one-variable function will appear as a curve instantly in most cases (if you have a fast computer), and if you are graphing a two-variable function with Function Grapher 3D the graph will be constructed as a surface by drawing a set of curves, namely, the x-direction and the y-direction contours.
		Similarly, when using Function Grapher 3D, to evaluate a two variable function at a particular point (x,y), input the x value and y value as constant expressions separated by comma in the text box provided.
	www.geocities.com /function.grapher/two-2-variable (733 words)

	Hyperbolic function (Site not responding. Last check: 2007-09-17)
		The parameter t should not be interpreted as an angle because it represents twice the area the x -axis the hyperbola and the straight line links the origin with the point (cosh t sinh t) on the hyperbola.
		The function cosh x is an even function that is symmetric with respect to y -axis and cosh 0 = 1
		The function sinh x is an odd function that is symmetric with respect to origin and sinh 0 = 0
	www.freeglossary.com /Sinh (549 words)

	MathViews - Functions
		The Blackman window function is used to reduce leakage in the output of a fast Fourier transform (FFT) to a greater degree than would be obtained from using a rectangular window function.
		function is identical to the sinw function except that the default value of the initial phase is 90 degrees rather than 0.
		function rounds the element(s) of its argument to the nearest integer towards 0.
	www.mathwizards.com /techinfo/man/mathv05.htm (4971 words)

	Hyperbolic Trigonometric Functions
		The McLaurin's series for the hyperbolic sine and cosine may be obtained from their definitions and the series for the exponential function.
		The McLaurin's series formulae for the hyperbolic arc sine, arc cosine, arc cotangent, arc secent, arc cosecent, arc versed sine, arc coverssed sine, and arc haversed sine are not interesting.
		The values of the inverse hyperbolic trigonometric functions have to be obtained from the foregoing arctangent, by solving the quadratic equations of the
	www.geocities.com /ResearchTriangle/2363/hyperbol.html (1630 words)

	Math 252-Appendix 1
		The hyperbolic sine and cosine functions are defined in terms of exponential functions as follows.
		The other hyperbolic functions tanh(x), sech(x), csch(x), coth(x) are defined as quotients of the hyperbolic sine and cosine in the same pattern as the trigonometric funtions.
		One practical application of the hyperbolic functions (which stems from properties of their derivatives), is to describe the shape of a hanging cable, such as a telephone line between telephone poles.
	oregonstate.edu /instruct/mth252h/Bogley/w02/A1.html (589 words)

	Hyperbolic Functions -- from Wolfram MathWorld
		hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cosecant,
		The hyperbolic functions share many properties with the corresponding circular functions.
		hyperbolic cosine function is the shape of a hanging cable (the so-called catenary).
	mathworld.wolfram.com /HyperbolicFunctions.html (256 words)

	Linear motor - Patent 6873066
		Alternatively, the hyperbolic function, in an XY coordinate system in which the central axis of each magnetic pole or each tooth opposite thereto is the X-axis, an axis perpendicular to the X-axis is the Y-axis, and the point of intersection of the X- and Y-axes is the origin, is given by
		The cogging torque is given in Newton (N), a unit of force, and the ratio is based on the shape represented by the hyperbolic function.
		However, the same effect can be obtained by using the shape represented by the reciprocal function of cosine in trigonometric function or the hyperbolic function for the external shape of each tooth or magnetic pole on the primary side.
	www.freepatentsonline.com /6873066.html (5008 words)

	Hyperbolic Functions
		The hyperbolic functions enjoy properties similar to the trigonometric functions; their definitions, though, are much more straightforward:
		The other hyperbolic functions are defined the same way, the rest of the trigonometric functions is defined:
		For every formula for the trigonometric functions, there is a similar (not necessary identical) formula for the hyperbolic functions:
	www.sosmath.com /trig/hyper/hyper01/hyper01.html (155 words)

	Hyperbolic Trigonometric Functions (Site not responding. Last check: 2007-09-17)
		We define the Arcsinh(x) function as the principal inverse of the hyperbolic sine function.
		This is a first-order ordinary differential-equation in the radius r = 1 / p as a function of the angle theta.
		The values of the inverse hyperbolic trigonometric functions have to be obtained from the foregoing arctangent, by solving the quadratic equations of the identities and
	www.rism.com /Trig/hyperbol.htm (9850 words)

	Karl's Calculus Tutor - Inverse Hyperbolics
		In the main text we found that the inverse hyperbolic functions, hyperbolic arcsine and hyperbolic arccosine, can appear as part of the integrals of certain quadratic-under-the-radical type of integrands.
		Observe that if you turned that on its side and took its mirror image, you would have the exact plot of hyperbolic tangent that you saw in the main text, indicating that this branch is indeed the inverse of hyperbolic tangent.
		Hyperbolic arcsine often appears in the integrals of functions that have a quadratic under the radical that has no real roots.
	www.karlscalculus.org /invhyper.html (928 words)

	Class jnt.functions.Bessel
		Evaluates the hyperbolic Bessel function of the first kind of order 0 for a given real argument x.
		Evaluates the hyperbolic Bessel function of the first kind of order 1 for a given real argument x.
		Evaluates the exponentially scalled hyperbolic Bessel function of the first kind of order 1 for a given real argument x.
	math.nist.gov /jnt/api/jnt.functions.Bessel.html (382 words)

	Atlas: Hyperbolic Function Theory by Sirkka-Liisa Eriksson (Site not responding. Last check: 2007-09-17)
		Around hundred years later Fueter defined regular functions in the algebra of quaternions and was able to prove the main theorems as Cauchy theorem, Cauchy formula and Laurent power series expansions.
		The key idea is that a regular function is a conjugate gradient of a harmonic function.
		is a conjugate gradient of a harmonic function in the sense of Hodge with respect a hyperbolic metric ds
	atlas-conferences.com /cgi-bin/abstract/casi-29 (264 words)

	Hyperbolic secant: Integration (subsection 21/01)
		Involving functions of the direct function, hyperbolic and trigonometric functions (24 formulas)
		Involving functions of the direct function, hyperbolic, exponential and trigonometric functions (26 formulas)
		Involving functions of the direct function, hyperbolic, exponential, trigonometric and a power functions (14 formulas)
	functions.wolfram.com /ElementaryFunctions/Sech/21/01 (207 words)

	3rd Year Honours Mathematical Physics Special Relativity Hyperbolic Trigonometric Functions
		You are familiar with ordinary trigonometric functions and their relation to complex numbers.
		Hyperbolic trigonometric functions are related to hyperbolae in a manner similar to that in which trigonometric functions are related to circles.
		Define the hyperbolic cosine, cosh, and the hyperbolic sine, sinh, in the following manner,
	www.thphys.may.ie /Notes/SR/hyperbolic/hyperbolic.html (269 words)

	Mathematical Models of the Hyperbolic Worlds
		for the hyperbolic Fibonacci and Lucas functions as:
		This theory is based on the hypothesis, that the geometry of phyllotaxis is hyperbolic, and the change of symmetry orders of phyllotaxis objects during their growth is based on the hyperbolic turn, the basic transforming motion of hyperbolic geometry.
		The article «Hyperbolic Universes with a Horned Topology and the CMB Anisotropy» [28] proved a great surprise to the authors because it showed that the geometry of the Universe is quite possibly is “shofarable” by its structure.
	www.mi.sanu.ac.yu /vismath/stakhov/index.html (5072 words)

	VINO 0.50 Manual - man3-3/math.3-3.txt
		Its properties are reflected fairly faithfully in the ele- mentary functions for a VAX distributed in 4.3 BSD.
		Some of the VMS functions are a little faster, some are a little more accurate, some are more puritanical about May 6, 1991 3 MATH(3) MATH(3) exceptions (like pow(0.0,0.0) and atan2(0.0,0.0)), and most occupy much more memory than their counterparts in libm.
		But simulating all three characteristics of an atomic function is still a tedious affair, entailing hosts of tests and saves-restores; work is under way to amelio- rate the inconvenience.
	www.eecs.harvard.edu /~vino/vino/release-0.50/man/man3-3/math.3-3.html (2538 words)

	Hyperbolic Trigonometry: A Crash Review
		Learn both trigonometry and hyperbolic trigonmetry so well that the identities cannot be confused.
		Hyperbolic trigonometric functions are defined in terms of the natural exponential function e
		Notation for powers and inverses of hyperbolic trigonmetric functions is similar to that of trigonometric functions:
	www.zaimoni.com /HyperbolicTrig.htm (316 words)

	Hyperbola - Wikipedia, the free encyclopedia
		For hyperbole, the figure of speech, see hyperbole.
		The rectangular hyperbola with the coordinate axes as its asymptotes is given by the equation xy=c, where c is a constant.
		Just as the sine and cosine functions give a parametric equation for the ellipse, so the hyperbolic sine and hyperbolic cosine give a parametric equation for the hyperbola.
	en.wikipedia.org /wiki/Hyperbolic (513 words)

	Accurate Assessment of {beta}-Cell Function: The Hyperbolic Correction -- Bergman et al. 51 (Supplement 1): 212 -- ...
		It is envisioned that, in the course of environmentally induced reductions in insulin sensitivity, "normal" pancreatic islets would respond by upregulation of the ß-cells’ sensitivity to glucose.
		However, no change in insulin secretion rate (horizontal arrow) or a reduction in insulin secretion rate (downward arrow) would indicate a reduction in islet function, as the DI would be reduced.
		If islet function were unchanged, data would be represented by the upward arrow—i.e., moving upward and to the left on a single hyperbola (solid line), and a constant DI.
	diabetes.diabetesjournals.org /cgi/content/full/51/suppl_1/S212 (4984 words)

	Hyperbolic Tangent
		The Hyperbolic Tangent function calculates the hyperbolic tangent of a value in radians.
		Where e is a transcendental number that is the base of natural logarithms and is equal to approximately 2.71828183.
		The function DegreesToRadians can be used to use this function with values in degrees.
	www.tradingsolutions.com /functions/HyperbolicTangent.html (85 words)

	Sample Configurable JCM Applet: SimpleGraph
		SimpleGraph is a configureable applet that shows the graph of a function and, optionally, marks a point on the graph.
		If there is a point, then the user can control its x-coordinate either by adjusting a slider at the bottom of the applet or by entering the x-coordinate in an input box.
		Furthermore, several new functions have been defined: The hyperbolic functions, "sinh(x)=(exp(x)-exp(-x))/2", "cosh(x)=(exp(x)+exp(x))/2", and "tanh(x)=sinh(x)/cosh(x)", have been added so that they can be used in expressions, even though they are not among the standard functions in the JCM parser.
	math.hws.edu /javamath/config_applets/SimpleGraph.html (484 words)

Try your search on: Qwika (all wikis)