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Topic: Airy function

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George Biddell Airy

George Airy

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	Airy function - Biocrawler (Site not responding. Last check: 2007-10-30)
		In mathematics, the Airy function Ai(x) is a special function, i.e., a function that appears so frequently that it deserves its own name.
		The function Ai(x) and the related function Bi(x), which is also called an Airy function, are solutions to the differential equation y'' − xy = 0.
		The Airy function is named after the British astronomer George Biddell Airy, who encountered it in his study of optics (Airy 1838).
	www.biocrawler.com /encyclopedia/Airy_function (631 words)

	George Biddell Airy - Wikipedia, the free encyclopedia
		He was born at Alnwick, one of a long line of Airys who traced their descent back to a family of the same name residing at Kentmere, in Westmorland, in the 14th century.
		Airy's discovery of a new inequality in the motions of Venus and the earth is in some respects his most remarkable achievement.
		In 1872 Airy conceived the idea of treating the lunar theory in a new way, and at the age of seventy-one he embarked on the prodigious toil which this scheme entailed.
	en.wikipedia.org /wiki/George_Biddell_Airy (1756 words)

	Function
		Additive function In coprime we have: f(ab) = f(a) + f(b).
		Meromorphic function A meromorphic function is a function that is singularities.
		Trapdoor function A trapdoor function is a cryptography.
	www.brainyencyclopedia.com /topics/function.html (2873 words)

	Maxima Manual
		This function is thus a canonical simplifier for sums of powers of SIN's and COS's of a particular type.
		sinfn and cosfn are functions of two arguments which are a coefficient and a trigonometric part of a term in series respectively.
		It is a predicate function of 6 arguments which are the coefficients of the U, V,..., Z in a term.
	www.delorie.com /gnu/docs/maxima/maxima_52.html (648 words)

	George Biddell Airy (Site not responding. Last check: 2007-10-30)
		The former are for the most part concerned with questions relating to the theory of light arising out of his professorial lectures, among which may be specially mentioned his paper "On the Diffraction of an Object-Glass with Circular Aperture." In 1831 the Copley Medal of the Royal Society was awarded to him) for these researches.
		In 1847 an altazimuth was erected, designed by Airy to enable observations of the moon to be made not only on the meridian, but whenever she might be visible.
		Their immediate result was to show that gravity at the bottom of the mine exceeded that at the top by 1918 6th of its amount, the depth being 1256 ft. From this he was led to the final value of 6-566 for the mean density of the earth as compared with that of water (Phil.
	www.wikiverse.org /george-biddell-airy (1663 words)

	Airy function -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-30)
		In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics, the Airy function Ai(x) is a (Click link for more info and facts about special function) special function, i.e., a function that appears so frequently that it deserves its own name.
		The function Ai(x) and the related function Bi(x), which is also called an Airy function, are solutions to the (An equation containing differentials of a function) differential equation.
		The Airy function is named after the British astronomer (Click link for more info and facts about George Biddell Airy) George Biddell Airy, who encountered it in his study of (The branch of physics that studies the physical properties of light) optics (Airy 1838).
	www.absoluteastronomy.com /encyclopedia/a/ai/airy_function.htm (763 words)

	Physics Today April 2001
		Some of these functions were (with one class of exceptions) known to mathematicians in 1964, but they were not well known to scientists, and had rarely been applied in physics.
		Functions of hypergeometric type can be ordered by the behavior of singular points of the differential equations representing them, or by a group-theoretical analysis of their symmetries.
		Of the two Airy functions, Ai is the one that decays towards infinity, while Bi grows; the J Bessel functions are regular at the origin, the Y Bessel functions have a pole or a branch point.
	www.physicstoday.org /pt/vol-54/iss-4/p11.html (1453 words)

	GNU Scientific Library -- Reference Manual
		If you are writing numerical functions in a program which also uses GSL code you may find it convenient to adopt the same error reporting conventions as in the library.
		This function converts the divided-difference representation of a polynomial to a Taylor expansion.
		The special functions are available in two calling conventions, a natural form which returns the numerical value of the function and an error-handling form which returns an error code.
	www.gnu.org /software/gsl/manual/gsl-ref.html (7698 words)

	[No title]
		This function is thus a canonical simplifier for sums of powers of SIN's and COS's of a particular type.
		In particular, all elliptic functions and integrals use the parameter m instead of the modulus k or the modular angle \alpha.
		The xi are merely dummy variables as in function definition headers and are used to indicate the ith argument of f.
	www.mit.edu /afs/athena/software/maxima/info/maxima.info-7 (4934 words)

	Airy function (Site not responding. Last check: 2007-10-30)
		is the differential equation which defines the Airy function.
		The Airy function is found as solution to boundary value problems in quantum mechanics and electromagnetic theory.
		Then the Airy function Ai(x) gives for a particle the quantum-mechanical amplitude.
	www.2dcurves.com /gamma/gammaa.html (106 words)

	GNU Scientific Library -- Reference Manual - Special Functions (Site not responding. Last check: 2007-10-30)
		The Debye functions are defined by the integral D_n(x) = n/x^n \int_0^x dt (t^n/(e^t - 1)).
		The hazard function for the normal distrbution, also known as the inverse Mill's ratio, is defined as h(x) = Z(x)/Q(x) = \sqrt{2/\pi \exp(-x^2 / 2) / \erfc(x/\sqrt 2)}.
		The transport functions J(n,x) are defined by the integral representations J(n,x) := \int_0^x dt t^n e^t /(e^t - 1)^2.
	jamesthornton.com /gnu/gsl/gsl-ref_7.html (6138 words)

	DLMF: Airy function; Rainbow (Site not responding. Last check: 2007-10-30)
		The faint line below the main colored arc is a 'supernumerary rainbow', produced by the interference of different sun-rays traversing a raindrop and emerging in the same direction.
		For each color, the intensity profile across the rainbow is an Airy function.
		Airy invented his function in 1838 precisely to describe this phenomenon more accurately than Young had done in 1800 when pointing out that supernumerary rainbows require the wave theory of light and are impossible to explain with Newton's picture of light as a stream of independent corpuscles.
	dlmf.nist.gov /Contents/ch11viz/rainbow.html~ (135 words)

	ipedia.com: Airy function Article (Site not responding. Last check: 2007-10-30)
		In mathematics, the main Airy functions Ai and Bi are defined as the two linearly independent solutions to the differential equation They can be written in integral form as follows : The Airy function...
		In mathematics, the main Airy functions Ai(x) and Bi(x) are defined as the two linearly independent solutions to the differential equation
		The Airy functions are common in physics and its applications; related Airy functions Gi(x) and Hi(x) also exist:
	www.ipedia.com /airy_function.html (142 words)

	DLMF: Bibliography (Site not responding. Last check: 2007-10-30)
		The Asymptotic Behaviour of the Inhomogeneous Airy Function
		On the Reversion of an Asymptotic Expansion and the Zeros of the Airy Functions.
		The Zeros and Maxima of the Airy Function and Its First Derivative to 25 Significant Figures.
	dlmf.nist.gov /Contents/AI/Bibliography.html (559 words)

	airy function - OneLook Dictionary Search (Site not responding. Last check: 2007-10-30)
		We found 2 dictionaries with English definitions that include the word airy function:
		Tip: Click on the first link on a line below to go directly to a page where "airy function" is defined.
		Airy Function : Eric Weisstein's World of Physics [home, info]
	www.onelook.com /?w=airy+function (81 words)

	GNU Scientific Library -- Reference Manual - Special Functions (Site not responding. Last check: 2007-10-30)
		These routines compute the normalize incomplete Beta function B_x(a,b)/B(a,b) for a > 0, b > 0, and @c{$0 \le x \le 1$} 0 <= x <= 1.
		This function computes an array of Gegenbauer polynomials C^{(\lambda)}_n(x) for n = 0, 1, 2, \dots, nmax, subject to \lambda > -1/2, @c{$nmax \ge 0$} nmax >= 0.
		This function computes an array of radial eigenfunctions L^{H3d}_l(\lambda, \eta) for @c{$0 \le l \le lmax$} 0 <= l <= lmax.
	www.ugcs.caltech.edu /info/gsl/gsl-ref_7.html (6059 words)

	airy :: Functions (MATLAB Function Reference)
		The Airy functions form a pair of linearly independent solutions to
		The relationship between the Airy and modified Bessel functions is
		successfully computed the Airy function for this element.
	www.mathworks.com /access/helpdesk/help/techdoc/ref/airy.html (134 words)

	c derivative functions (Site not responding. Last check: 2007-10-30)
		Banking customers are finally having a say and a greater understanding as to what happens to their well earned money.
		The derivative of a function at a certain point is a measure of the rate at which that function is changing as an argument undergoes change.
		AID (DAID) Derivative of the Airy function Ai(x...
	www.financial-repeater1.com /articles/42/c---derivative-functions.html (498 words)

	airy (MATLAB Function Reference) (Site not responding. Last check: 2007-10-30)
		The Airy functions form a pair of linearly independent solutions to:
		The relationship between the Airy and modified Bessel functions is:
		returns the Airy function, Ai(Z), for each element of the complex array
	www.haystack.edu /computing/matlab5.3.1/help/techdoc/ref/airy.html (92 words)

	Airy function (exact WKB results for potentials of odd degree) (ResearchIndex) (Site not responding. Last check: 2007-10-30)
		Airy function (exact WKB results for potentials of odd degree) (ResearchIndex)
		Airy function (exact WKB results for potentials of odd degree)
		1 the functional equation f (context) - Sibuya
	citeseer.ist.psu.edu /174825.html (186 words)

	MATLAB Central File Exchange - Airy Function Generator
		MATLAB Central File Exchange - Airy Function Generator
		MATLAB Central > File Exchange > Image Processing > Application > Airy Function Generator
		This function creates a simple solid circle defined by the user and then preforms a fourier transform upon the array such that the putput is an airy disk for the given circle,
	www.mathworks.com /matlabcentral/fileexchange/loadFile.do?objectId=12355&objectType=FILE (224 words)

	Special Functions (Site not responding. Last check: 2007-10-30)
		A package in the SHARE directory for numerical routines for Elliptic Functions and Complete Elliptic Integrals.
		This function is related to the complex error function by
		If you want the Rational Function Package to know about
	starship.python.net /crew/mike/maxima/html/macref/node25.html (454 words)

	DELIB: Airy function
		Mathworld Digital math library Encyclopedia of Special Functions Abramowitz and Stegun
		M. Abramowitz and I. Stegun (Eds.) (1964), Handbook of Mathematical Functions, National Bureau of Standards Applied Mathematics Series No. 55.
		An Introduction to the Classical Functions of Mathematical Physics, John Wiley & Sons, New York.
	www.mathtable.com /delib/airyfunction.php (140 words)

	airy (Site not responding. Last check: 2007-10-30)
		This content dictionary contains symbols to describe the Airy functions and associated functions.
		Ai The symbol Ai defines the unary Airy Ai function; as in Abramovitz and Stegun equation 10.4.1.
		Bi The symbol Bi defines the unary Airy Bi function.
	www.openmath.org /cocoon/openmath/cdfiles/contrib/cd/airy.html (410 words)

	MATLAB Central File Exchange - Airy Function Generator
		MATLAB Central > File Exchange > Image Processing > Application > Airy Function Generator > Code Metrics
		You can also score your own files before submission by downloading the code metrics zip file.
		Function name 'CircSignal' will be known to MATLAB by its file name: 'airy'.
	www.mathworks.com /matlabcentral/fileexchange/loadFile.do?objectId=12355&objectType=scoreDetails (239 words)

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