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Topic: Hyperbolic tangent

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Holomorphic

Sigmoid function

Riemann zeta function

Trigonometric function

	Hyperbolic function - Wikipedia, the free encyclopedia
		In mathematics, the hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.
		The basic hyperbolic functions are the hyperbolic sine sinh, and the hyperbolic cosine cosh, from which are derived the hyperbolic tangent tanh, etc.
		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.
	www.wikipedia.org /wiki/Hyperbolic_function (498 words)

	hyperbolic functions -- Encyclopædia Britannica (Site not responding. Last check: 2007-10-25)
		also called hyperbolic trigonometric functions the hyperbolic sine of z (written sinh z); the hyperbolic cosine of z (cosh z); the hyperbolic tangent of z (tanh z); and the hyperbolic cosecant, secant, and cotangent of z.
		the hyperbolic sine of z (written sinh z); the hyperbolic cosine of z (cosh z); the hyperbolic tangent of z (tanh z); and the hyperbolic cosecant, secant, and cotangent of z.
		The first description of hyperbolic geometry was given in the context of Euclid's postulates, and it was soon proved that all hyperbolic geometries differ only in scale (in the same sense that spheres only differ in size).
	www.britannica.com /eb/article-9041791 (866 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.
		And to further contrast the hyperbolic with the trig, note that the trig function, tangent, is unbounded and has undefined points on its domain.
		The integrands that the hyperbolic functions address are all analogs of the ones that the trig functions were able to address.
	www.karlscalculus.org /hyper.html (2129 words)

	Hyperbolic function
		The hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.
		However, the parameter t should not be interpreted as an angle, and the hyperbolic functions are not periodic.
		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.
	news-server.org /h/hy/hyperbolic_function.html (307 words)

	Tutorial 4
		There are four functions supported by the applet: linear, sigmoid, exponential, and hyperbolic tangent.
		A hyperbolic tangent function is similar to a sigmoid, but it maps all of its input to [-1,1].
		The linear activation function does not suffer from this problem, but since it is not a "squashing" function (the sigmoid and hyperbolic tangent has finite ranges), it also has numerical problems with large training sets as all the sum of squares errors add up to large numbers.
	www.cs.ubc.ca /labs/lci/CIspace/Version4/neural/help/tutorial4.html (617 words)

	Hyperbolic functions (Site not responding. Last check: 2007-10-25)
		Hyperbolic functions are found useful in two main areas:
		On the Pickett N 4P-T, the hyperbolic functions are on the slide, not the stock.
		On the K and E this calculation is not quite so easy as it involves use of the C scale on the opposite face of the rule but similar principles apply.
	www.sliderules.clara.net /a-to-z/hyperbolic.htm (387 words)

	Exponents (Site not responding. Last check: 2007-10-25)
		The hyperbolic functions can be defined in terms of exponentials.
		An application of the hyperbolic tangent is in calculating the speed of ocean waves.
		The hyperbolic cosine and its inverse are encountered in fluid friction in the case of quadratic drag.
	hyperphysics.phy-astr.gsu.edu /hbase/exp.html (151 words)

	Hyperbolic function (Site not responding. Last check: 2007-10-25)
		Complex Manifolds and Hyperbolic Geometry: II Iberoamerican Congress on Geometry, January 4-9, 2001, Cimat, Guanajuato, Mexico (Contemporary Mathematics (American Mathematical Society), Vol 311)
		This book is intended to introduce readers to Hyperbolic Geometry in 3 dimensions.
		The book covers from a review of hyperbolic surfaces to the classification program of 3-manifold initiated by Thurston....
	www.freeglossary.com /Hyperbolic_function (549 words)

	Amplifier and method of canceling distortion by combining hyperbolic tangent and hyperbolic sine transfer functions - ... (Site not responding. Last check: 2007-10-25)
		a hyperbolic tangent (tan h) amplifier having first and second inputs coupled for receiving the differential input signal and first and second outputs respectively coupled to the first and second summation nodes; and
		a hyperbolic sine (sin h) amplifier having first and second inputs coupled for receiving the differential input signal and first and second outputs respectively coupled to the first and second summation nodes.
		The present invention relates in general to amplifiers and, more particularly, to an amplifier which combines a hyperbolic tangent transfer function with a hyperbolic sine transfer function to cancel distortion.
	www.freepatentsonline.com /5942939.html (3522 words)

	Karl's Calculus Tutor - Inverse Hyperbolics
		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.
		This extended version of hyperbolic arctangent can be used for integrating functions that have a quadratic with real roots in the denominator, but no radical.
		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)

	Hyperbolic Function (Site not responding. Last check: 2007-10-25)
		He came up with a spun-aluminum housing in the shape of a hyperbolic funnel; three cork-ball-tipped metal rods serve as feet...
		is it is accurate in implication (if understandably hyperbolic in formulation).
		Certainly it's a hyperbolic statement, but it's closer to the mark than the Cubs may...
	www.wikiverse.org /hyperbolic-function (439 words)

	Hyperbolic function : Hyperbolic tangent
		sinh x = (exp(x) - exp(-x))/2 (hyperbolic sine, pronounced "shine" or "sinch") cosh x = (exp(x) + exp(-x))/2 (hyperbolic cosine, pronounced "cosh") tanh x = sinh(x)/cosh(x) (hyperbolic tangent, pronounced "tanch") coth x = cosh(x)/sinh(x) (byperbolic cotangent, pronounced "coth") sech x = 1/cosh(x) (byperbolic secant, pronounced "sech") csch x = 1/sinh(x) (hyperbolic cosecant, pronounced "cosech")
		Just as the points (cos x, sin x) define a circle, the points (cosh x, sinh x) define a hyperbola because of the formula
		The parameter x can no longer be interpreted as an angle, though, and the hyperbolic functions are not periodic.
	www.fastload.org /hy/Hyperbolic_tangent.html (396 words)

	hyperbolic-tangent-stretching (Site not responding. Last check: 2007-10-25)
		When there is no curve, the grid size is computed under the assumtion that the grid line has unit length and is uniformly parametrized.
		Use the default parameters for the hyperbolic tangent stretching.
		Stop changing the parameters of the hyperbolic tangent stretching and exit from this command level.
	www.na.chalmers.se /~andersp/xcog/xcog_users_guide/node29.html (105 words)

	Hyperbolic Functions - Part 1: Introduction (Site not responding. Last check: 2007-10-25)
		These two functions are called the hyperbolic cosine and the hyperbolic sine respectively and together are called the hyperbolic functions.
		These functiosn, although not as useful as the trigonometric functions for working with angles, are howevr very useful when it comes to integration because of the many hyperbolic identities.
		For thsi reason other hyperbolic functions are also defined; the hyperbolic tangent, cotangent, secant and cosecant.
	people.bath.ac.uk /ma3jtp/hyperbolics/part1.html (223 words)

	3rd Year Honours Mathematical Physics Special Relativity Hyperbolic Trigonometric Functions
		The behaviour of sin and cos under differentiation can also be determined easily from the exponential representation.
		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)

	hyperbolic trigonometry (Site not responding. Last check: 2007-10-25)
		the hyperbolic lengths of the sides of hyperbolic triangles.
		A for the angle at vertex A, i.e.
		In hyperbolic geometry, we have the (AAA) condition for h-congruence.
	www.maths.gla.ac.uk /~wws/cabripages/hyperbolic/hypertrig.html (337 words)

	Reference
		Return the arc sine, arc cosine, arc tangent of x, taking account of the specified units of angle
		Return the hyperbolic sine, hyperbolic cosine, hyperbolic tangent of x
		Return the inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent of x
	rcalc.sourceforge.net /doc/rcalc-reference.html (115 words)

	HYPERBOLIC TANGENT ACTIVATION FUNCTION (TANH) IN ARTIFICIAL NEURAL NETWORKS - Knowledge Discovery Keys
		The hyperbolic sine functon sinh(x) is defined by
		The hyperbolic cosine function cosh(x) is defined as the derivative of the hyperbolic sine function sinh(x) where
		The hyperbolic tangent tanh(x) = sinh(x)/cosh(x) where sinh(x) is defined in equation 1 and cosh(x) is defined in equation 2c, therefore
	www.kdkeys.net /forums/3715/ShowPost.aspx (267 words)

	Hyperbolic Trigonometric Functions
		The MacLaurin's series for the hyperbolic sine and cosine may be obtained from their definitions and the series for the exponential function.
		The MacLaurin's series formulae for the hyperbolic arc sine, arc cosine, arc cotangent, arc secant, arc cosecant, arc versed sine, arc coversed 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 identities and
	www.rism.com /Trig/hyperbol.htm (9675 words)

	ATanH MathTrigComplex Function -- Entisoft Tools 2.0 Object Library (Site not responding. Last check: 2007-10-25)
		Angle whose hyperbolic tangent is X. Inverse of the TanH function.
		vX: Function returns the principal value of the angle whose hyperbolic tangent (expressed in radians) is vX.
		Function returns Null if vX is Null or cannot be fixed up to a real or complex number (as defined by the ComplexStringToReals function).
	www.entisoft.com /ESTools/MathTrigComplex_ATanH.HTML (154 words)

	TANH: Hyperbolic tangent transfer function (Site not responding. Last check: 2007-10-25)
		Defines a hyperbolic tangent, or soft limiting, transfer function.
		There is no corresponding capability in any SPICE that I know of, but you can get close with POLY.
		This function describes a hyperbolic tangent transfer function similar to what you get with a single stage push-pull amplifier, or a simple CMOS inverter acting as an amplifier.
	www.gnucap.org /gnucap-man-html/gnucap-man098.html (147 words)

	Hyperbolic Tangent
		The Hyperbolic Tangent function calculates the hyperbolic tangent of a value in radians.
		The value of the hyperbolic tangent is equal to:
		Where e is a transcendental number that is the base of natural logarithms and is equal to approximately 2.71828183.
	www.tradingsolutions.com /functions/HyperbolicTangent.html (85 words)

	efg's Mathematics Projects -- Complex Hyperbolic Functions
		This page shows how to compute several complex hyperbolic functions, including hyperbolic cosine, hyperbolic sine, hyperbolic tangent, hyperbolic secant, hyperbolic cosecant, and hyperbolic cotangent.
		Complex hyperbolic tangent: CTanh = Tanh(z) = Sinh(z)/Cosh(z)
		Complex hyperbolic cotangent: CCoth = Coth(z) = Cosh(z)/Sinh(z)
	www.efg2.com /Lab/Mathematics/Complex/Hyperbolic.htm (1461 words)

	Algae: Standard Functions (Site not responding. Last check: 2007-10-25)
		function returns the hyperbolic arc cosine of its numeric argument.
		function returns the hyperbolic arc tangent of its numeric argument.
		function returns the hyperbolic tangent of its numeric argument.
	www.eskimo.com /~ksh/algae/algae_6.html (11166 words)

	CARM User's Guide: tanh Library Routine
		#include double tanh (double x); /* value to calc hyperbolic tangent for */
		The tanh function calculates the hyperbolic tangent for the floating-point value
		The tanh function returns the hyperbolic tangent of
	www.keil.com /support/man/docs/ca/ca_tanh.htm (77 words)

	Data Conditioning for Neural Networks — A Letter to the Editor (Site not responding. Last check: 2007-10-25)
		About four years ago, when I was experimenting with different transfer functions, I realized that I was wasting a lot of computer time with the hyperbolic tangent function.
		If you take this function, add 1 to it, then divide by 2, the result is the same as if you used the sigmoid function with twice the input.
		Bob Martin is correct when he identifies the hyperbolic tangent function (TanH) as a shifted and scaled sigmoid function.
	www.day-trading-commodities.com /data.asp (460 words)

	Douglas Baldwin
		Göktas, W. Hereman, Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations, Computer Physics communications, vol.
		The software, PDESpecialSolutions.m, allows for the computation of solutions expressible in hyperbolic tangent, hyperbolic secant, and Jacobi ellitpic functions.
		For more information, see our paper Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations.
	www.mines.edu /students/d/dbaldwin (451 words)

	The GNU C Library (Site not responding. Last check: 2007-10-25)
		The functions in this section are related to the exponential functions; see Exponents and Logarithms.
		There are counterparts for the hyperbolic functions which take complex arguments.
		These functions return the inverse complex hyperbolic tangent of
	www.jamesthornton.com /gnu/glibc/Hyperbolic-Functions.html (143 words)

	The Hyperbolic Tangent Function (Site not responding. Last check: 2007-10-25)
		The hyperbolic tangent function is one of the hyperbolic transcendental functions.
		Its definition is in terms of the cosh and sinh functions.
		Often the series expansion of the function can be found and recognized.
	www.cobalt.chem.ucalgary.ca /ziegler/chm373/rudiment/mathbas/tanh.htm (58 words)

	Hyperbolic Functions (Site not responding. Last check: 2007-10-25)
		This function returns the inverse hyperbolic sine of
		This function returns the inverse hyperbolic cosine of
		This function returns the inverse hyperbolic tangent of
	chaos.phy.ohiou.edu /~thomas/ref/info/libc/Hyperbolic_Functions.html (55 words)

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