
	Where results make sense

Topic: An infinitely differentiable function that is not analytic

Related Topics

Complex analysis

North Pole

Contest of Champions

Dino Jelusic

Chicken Ranch

Schlumberger Limited

First Great Awakening

Colin Farrell

List of cities in Canada

	PlanetMath: analytic
		Because of this equivalence, an analytic function in the complex case is often defined to be one that is holomorphic, instead of one having a Taylor series as above.
		Although the two definitions are equivalent, it is not an easy matter to prove their equivalence, and a reader who does not yet have this result available will have to pay attention as to which definition of analytic is being used.
		This is version 5 of analytic, born on 2001-12-28, modified 2004-10-24.
	planetmath.org /encyclopedia/Analytic.html (162 words)

	Smooth function - Wikipedia, the free encyclopedia
		For example, the exponential function is evidently smooth because the derivative of the exponential function is the exponential function itself.
		Smooth functions with given closed support are used in the construction of smooth partitions of unity (see topology glossary for partition of unity); these are essential in the study of smooth manifolds, for example to show that Riemannian metrics can be defined globally starting from their local existence.
		From what has just been said, partitions of unity don't apply to holomorphic functions; their different behaviour relative to existence and analytic continuation is one of the roots of sheaf theory.
	www.encyclopedia-online.info /Smooth (535 words)

	Analytic function (Site not responding. Last check: 2007-10-22)
		In mathematics, an analytic function is one that is locally given by a convergent power series.
		Complex analysis teaches us that if a function f is differentiable in some open disk D centered at a point c in the complex field, then it necessarily has derivatives of all orders in that same open neighborhood, and the power series
		That is an important respect in which complex functions are better-behaved than real functions; see an infinitely differentiable function that is not analytic.
	bopedia.com /en/wikipedia/a/an/analytic_function.html (112 words)

	An infinitely differentiable function that is not... - Wikipedia, the free encyclopedia
		Please search for An infinitely differentiable function that is not...
		Look for An infinitely differentiable function that is not...
		Promotional articles about yourself, your friends, your company or products; or articles written as part of a marketing or promotional campaign, may be deleted in accordance with our deletion policies.
	en.wikipedia.org /wiki/An_infinitely_differentiable_function_that_is_not... (184 words)

	Smooth function - Gurupedia
		continuous function; such functions are also called continuously differentiable.
		Smooth functions with given closed support are used in the construction of smooth partitions of unity (see topology glossary for partition of unity); these are essential in the study of
		holomorphic functions; their different behaviour relative to existence and analytic continuation is one of the roots of sheaf theory.
	www.gurupedia.com /s/sm/smooth_function.htm (493 words)

	Analytic function (Site not responding. Last check: 2007-10-22)
		Complex analysis teaches us that if a function f of one complex variable is differentiable in some open disk D centered at a point c in the complex field, then it necessarily has derivatives of all orders in that same open neighborhood, and the power series
		A complex analytic function of several complex variables is defined to be analytic and holomorphic at a point if it is locally expandable (within a polydisk, a cartesian product of disks, centered at that point) as a convergent power series in the variables.
		A real function of a real variable given locally by a power series is a real analytic function.
	www.free-download-soft.com /info/analytic-function.html (247 words)

	Real Analysis
		Infinite series, which are special sequences, are also studied at this point.
		They are # a measurable set is ''almost'' an open set; # a measurable function is ''almost'' a continuous function; and # a convergent series is ''almost'' uniformly convergent.
		An analysis is a critical evaluation, usually made by breaking a subject (either material or intellectual) down into its constituent parts, then describing the parts and their relationship to the whole.
	www.artistbooking.com /trips/163/real-analysis.html (1112 words)

	smooth information,smooth (Site not responding. Last check: 2007-10-22)
		For example, the exponential function is evidentlysmooth because the derivative of the exponential function is the exponential function itself.
		smooth functions with given closed support are used in the construction ofsmooth partitions of unity (see topologyglossary for partition of unity); these are essential in the study of smooth manifolds, for example to show that Riemannian metrics can be defined globally starting from their local existence.
		Given a number of overlapping intervals on the line, bump functions can be constructed on each of them, and on semi-infiniteintervals (-∞, c] and [d,+∞) to cover the whole line, such that the sum of the functions is always1.
	www.vsearchmedia.com /smooth.html (567 words)

	More on Smoothness
		A function is called C1 if it has a derivative that is a continuous function; such functions are also called continuously differentiable.
		A function is called Cn for n ≥ 1 if it can be differentiated n times, with a continuous n-th derivative.
		The smooth functions are therefore those that lie in the class Cn for all n.
	www.artilifes.com /smoothness.htm (701 words)

	smotoh information,smooth (Site not responding. Last check: 2007-10-22)
		In mathematics, a smotoh function is one that isinfinitely differentiable, i.e., has derivatives of all finite orders.
		For example, the exponential function is evidentlysmotoh because the derivative of the exponential function is the exponential function itself.
		smotoh functions with given closed support are used in the construction ofsmotoh partitions of unity (see topologyglossary for partition of unity); these are essential in the study of smotoh manifolds, for example to show that Riemannian metrics can be defined globally starting from their local existence.
	www.vsearchmedia.com /smotoh.html (567 words)

	COURSE: Advanced Calculus (MATH 452) (Site not responding. Last check: 2007-10-22)
		The elementary functions as solutions of ODE's: The natural logarithm & exponential functions.
		Example: An infinitely differentiable function that is not analytic.
		Pointwise & uniform convergence of sequences of functions.
	people.wwc.edu /staff/thomth/452/452w00h.htm (111 words)

	[No title]
		An elegant rearrangement of a conditionally convergent iterated integral
		An Eye for an Eye: The Untold Story of Jewish Revenge Against Germans in 1945
		An Historical Account of Two Notable Corruptions of Scripture
	www.knowledgefun.com /book/a/an (155 words)

	Mathematics Numerical Analysis Homework Help
		Also prove that there is no neighbourhood I of 0 such that the function f:I->R is increasing.
		Suppose that the function F:R->R has derivatives of all orders and that: F"(x) - F'(x) - F(x) = 0 for all x F(0)=1 and F'(0)=1 Find a recursive formula for the coefficients of the nth Taylor polynomial for F:R->R at x=0.
		Use the given information: the functions g:[a,b]->R and h:[a,b]->R are continuous with h(x) >= 0 for all x in [a,b], and there is a point c in (a,b) such that: the integral from a to b of h(x)g(x)dx = g(c) times the integral from a to b of h(x)dx.
	www.brainmass.com /homeworkhelp/math/numericalanalysis/pg1 (460 words)

	An infinitely differentiable function that is not... - physics -An infinitely differentiable function that is not... (Site not responding. Last check: 2007-10-22)
		- physics -An infinitely differentiable function that is not...
		If you created an article under this title previously, it may have been deleted.
		See candidates for speedy deletion for possible reasons.
	physikweb.de /physics/index.php/An_infinitely_differentiable_function_that_is_not... (164 words)

	Anadolu Pop hall and oates Anadolu Pop
		Buy items individually or save money with a Moviso monthly savings package!
		An Nisa An Infinitely Differentiable Function That Is Not Analytic
		Anadolu Pop is a musical style created by Murat Ses of Mogollar in the late 1960s and early 1970s.
	www.find-ask.com /Encyclopedia/Anadolu_Pop/Anadolu_Pop.html (290 words)

	Mathematics Numerical Analysis Homework Help
		the functions g:[a,b]->R and h:[a,b]->R are continuous with h(x) >= 0 for all x in [a,b], and there is a point c in (a,b) such that:
		to show that the Cauchy Integral Remainder Theorem implies the Lagrange Remainder Theorem if the function f^(n+1):I->R is assumed to be continuous.
		Since 2001, BrainMass.com has been the world's premier homework help service.
	www.brainmass.com /homeworkhelp/math/numericalanalysis/11036 (159 words)

Try your search on: Qwika (all wikis)