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Topic: Gudermannian function

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	Gudermannian function - Wikipedia, the free encyclopedia
		Gudermannian function with its asymptotes y = ±π/2 marked in gray.
		The Gudermannian function, named after Christoph Gudermann (1798 - 1852), relates the circular and hyperbolic trigonometric functions without resorting to complex numbers.
		The derivatives of the Gudermannian and its inverse are
	en.wikipedia.org /wiki/Gudermannian_function (68 words)

	CONK! Encyclopedia: List_of_functions (Site not responding. Last check: 2007-10-21)
		A modern, abstract point of view contrasts large function spaces, which are infinite-dimensional and within which most functions are 'anonymous', with special functions picked out by properties such as symmetry, or relationship to harmonic analysis and group representations.
		Subadditive function: The value of a sum is less than or equal to the sum of the values of the summands.
		Superadditive function: The value of a sum is greater than or equal to the sum of the values of the summands.
	www.conk.com /search/encyclopedia.cgi?q=List_of_functions (761 words)

	Tangent half-angle formula - Wikipedia, the free encyclopedia
		In various applications of trigonometry, it is useful to rewrite the trigonometric functions (such as sine and cosine) in terms of rational functions of a new variable t.
		These identities can be useful in calculus for converting rational functions in sine and cosine to functions of t in order to find their antiderivatives.
		The Gudermannian function gives a direct relationship between the circular functions and the hyperbolic ones that does not involve complex numbers.
	en.wikipedia.org /wiki/Tangent_half-angle_formula (499 words)

	Zeno: Language reference (Site not responding. Last check: 2007-10-21)
		Function returns the minute of the current hour as an integer corresponding to the argument which is assumed to be the total number of seconds since January 1, 1601, 00:00:00.
		Function returns the number of milliseconds of the current second as an integer corresponding to the argument which is assumed to be the total number of seconds since January 1, 1601, 00:00:00.
		Function returns the second of the current minute as an integer corresponding to the argument which is assumed to be the total number of seconds since January 1, 1601, 00:00:00.
	home.att.net /~srschmitt/zeno_B.html (3385 words)

	Partial list of calc builtin functions
		The quomod function is used to obtain both the quotient and remainder of a division in one operation.
		The digit and bit functions return individual digits of a number, either in base 10 or in base 2, where the lowest digit of a number is at digit position 0.
		The functions rcin, rcmul, rcout, rcpow, and rcsq are used to perform modular arithmetic calculations for large odd numbers faster than the usual methods.
	www.isthe.com /chongo/tech/comp/calc/calc-builtin.html (1218 words)

	[No title]
		to correspond to the definition of the mathematical function.
		Input, integer N, the argument of the function.
		The Gudermannian function relates the hyperbolic and trigonomentric !
	www.csit.fsu.edu /~burkardt/f_src/polpak/polpak.f90 (2195 words)

	Gudermannian function -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		Gudermannian function -- Facts, Info, and Encyclopedia article
		The (Something inverted in sequence or character or effect) inverse Gudermannian function is given by
		The ((linguistics) a word that is derived from another word) derivatives of the Gudermannian and its inverse are
	www.absoluteastronomy.com /encyclopedia/g/gu/gudermannian_function.htm (98 words)

	List of mathematical functions
		Constant function: a fixed value regardless of arguments.
		Euler's phi function: Number of numbers coprime to (and not bigger than) a given one.
		Baudoin, the half-caste, who for some time had appeared oppressed with a the desponding air of the man, asked him kindly and repeatedly the cause the interest he took in him, maintained the most absolute silence and scene, which took place about noon in the house in the Rue de Clichy that morning with Adrienne.
	www.datamass.net /li/list-of-mathematical-functions.html (573 words)

	Tractrix . Gudermannian function . Trigonometric function . Natural logarithm . Cartesian coordinate system (Site not responding. Last check: 2007-10-21)
		The trigonometric functions are periodic, so we must restrict their domains before we are able to define a unique inverse.
		In the following, the functions on the left are defined by the...
		The natural logarithm is the logarithm to the base e mathematical constant e, where e is approximately equal to 2.71828 no exact fraction can be given, as e is an irrational number just like...
	www.uk.fraquisanto.net /Tractrix (311 words)

	Footnotes (Site not responding. Last check: 2007-10-21)
		This paper's regression problem is called the ``inverse Gudermannian'', referred to here simply as the ``Gudermannian''.
		Lawn-RPBR (no memory) and Lawn-RPBR-X (useless memory functions) are not shown because memory is required for the problem.
		Zero is especially likely to occur with a function set such as this where aspects of it, like boolean functions and the initally all zeroed valued memory, contribute to the likliness of zero as a value
	www.cs.cmu.edu /afs/cs/usr/astro/mosaic/TellerGP96/footnode.html (70 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		function [ n_data, x, fx ] = gud_values (n_data) %% GUD_VALUES returns some values of the Gudermannian function.
		% % Discussion: % % The Gudermannian function relates the hyperbolic and trigonomentric % functions.
		% % This value GD is called the Gudermannian of X and symbolized % GD(X).
	www.csit.fsu.edu /~burkardt/m_src/test_values/gud_values.m (191 words)

	Negative Results with MBPR
		Table 3 shows the basic function set that all the regression problems discussed in this paper used (except where explicitly noted).
		The relative simplicity of the function set was an important factor in the decision to choose regression as our third problem domain.
		Table 3:1 presents the results of the first set of regression runs with the Gudermannian function and 20 indexed memory units.
	www.cs.cmu.edu /afs/cs/usr/astro/mosaic/TellerGP96/node8.html (615 words)

	[No title]
		Definition: The Gudermannian function relates the hyperbolic and trigonomentric functions.
		This value GAMMA(X) is called the Gudermannian of X. The inverse Gudermannian function is given as input a value GAMMA and computes the corresponding value X. Modified: 08 April 1999 Author: John Burkardt Parameters: Input, float GAMMA, the value of the Gudermannian.
		The ATAN function by contrast always returns an angle in the first or fourth quadrants.
	orion.math.iastate.edu /burkardt/c_src/subpakc/subpakc.c (5641 words)

	Elementary Transcendental Functions
		You can find the numerical values of mathematical functions to any precision.
		The arguments of trigonometric functions are always given in radians.
		Here is a plot of the hyperbolic tangent function.
	documents.wolfram.com /v4/MainBook/3.2.6.html (64 words)

	Integral (Site not responding. Last check: 2007-10-21)
		Nonzero may be expressed as finite integrals over transformed functions.
		If the analytic form of a function is known (instead of its values merely being tabulated at a fixed number of points), the best numerical method of integration is called
		Abscissas at which to compute the function, Gaussian quadrature produces the most accurate approximations possible.
	mathserver.sdu.edu.cn /mathency/math/i/i143.htm (402 words)

	[No title]
		Gudermannian function is given as input a value GAMMA and computes !
		Since a library function ASINH may be available on some systems, !
		function by contrast always returns an angle in the first or fourth !
	orion.math.iastate.edu /burkardt/f_src/subpak/subpak.f90 (3351 words)

	The Mathematica Book Online: Advanced Mathematics in Mathematica \| Mathematical Functions
		Mathematica gives exact results for logarithms whenever it can.
		You can convert from degrees by explicitly multiplying by the constant Degree.
		There are a number of additional trigonometric and hyperbolic functions that are sometimes used.
	documents.wolfram.com /mathematica/book/section-3.2.7 (75 words)

	gudermannian (Site not responding. Last check: 2007-10-21)
		The gudermannian is a combination of a tangent and the exponential function.
		We see often a supplementary factor 2 and constant -
		The inverse of the gudermannian function can be written as a combination of the natural logarithm, the secant and the tangent:
	www.2dcurves.com /exponential/exponentialgu.html (43 words)

	[No title]
		It is the inverse Gudermannian function: gd^-1 (x).
		If my mouse is on the point (100,100) and > I want to calculate lat and lon I don't know what to do.
		Longitude is indeed > a linear function, so that is no problem.
	www.math.niu.edu /~rusin/known-math/99/mercator (833 words)

	Spatial News [gislist] finding the y of a latitude for a mercator projection Archives
		However, when I am plotting points on a map which is not a world map, I
		cannot figure out how to scale the gudermannian values so that they are
		Essentially when I have a map whose latitude boundings are 70N 30N, I
	spatialnews.geocomm.com /community/lists/viewmessage.phtml?id=31918 (262 words)

	GMT Mailing List: Re: [GMT-HELP] Convergence (Site not responding. Last check: 2007-10-21)
		radians, which is indeed the inverse Gudermannian function.
		One ends up with the integral of the
		> secant function, which is related to the inverse (if I remember)
	wegener.mechanik.tu-darmstadt.de /GMT-Help/Archiv/12620.html (229 words)

	Applied Mathematics Series 55
		Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables (AMS55)
		Purchase the electronic edition of this book in Adobe PDF format!
		Bernoulli and Euler Polynomials, Riemann Zeta Function (p.
	www.convertit.com /go/convertit/reference/ams55.asp?Res=200&Page=77 (466 words)

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