
	Where results make sense

Topic: Functional equation

Related Topics

List of equations

Ordinary differential equation

Integral equation

Biquadratic equation

Partial differential equation

Solution point

Diophantine equation

Inequality

In the News (Sat 2 Jun 12)

EXECUTIVE POWER

Iran

ANALYSIS

Pakistan

Family compact

	Functional equation (L-function) - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-08)
		Therefore use of the functional equation is basic, in order to study the zeta-function in the whole complex plane.
		A unified theory of such functional equations was given by Erich Hecke, and the theory taken up again in Tate's thesis by John Tate.
		There are also functional equations for the local zeta-functions, arising at a fundamental level for the (analogue of) Poincaré duality in étale cohomology.
	en.wikipedia.org /wiki/Functional_equation_(L-function) (580 words)

	PlanetMath: functional equation (Site not responding. Last check: 2007-10-08)
		A functional equation is an equation whose unknowns are functions.
		Functional equations appear many places, for example, the gamma function and Riemann's zeta function both satisfy functional equations.
		This is version 4 of functional equation, born on 2002-10-24, modified 2003-06-15.
	planetmath.org /encyclopedia/FunctionalEquation.html (97 words)

	39: Difference and functional equations
		When the focus of a functional equation is on continuity of functions and a domain is specified, this becomes a question of topology (in particular this sometimes becomes questions about the group of homeomorphism or diffeomorphisms of a set.
		Functions whose domains are integers are sequences, of course; thus a functional equation with this domain is essentially a recursion problem.
		Functional equations are often studied by considering the orbits of points in the domain under iterates of some function.
	www.math.niu.edu /~rusin/known-math/index/39-XX.html (583 words)

	Functional equation - Wikipedia, the free encyclopedia
		In mathematics or its applications, a functional equation is an equation in terms of independent variables, and also unknown functions, which are to be solved for.
		Many properties of functions can be determined by studying the types of functional equations they satisfy.
		Usually the term functional equation is reserved for equations that are not in some simple sense reducible to algebraic equations, often because two or more known functions of the variables are substituted as arguments into an unknown function to be solved for.
	en.wikipedia.org /wiki/Functional_equation (363 words)

	Encyclopedia: Functional equation (Site not responding. Last check: 2007-10-08)
		In mathematics, a function is a relation, such that each element of a set (the domain) is associated with a unique element of another (possibly the same) set (the codomain, not to be confused with the range).
		In mathematics, the Riemann zeta function is a function which is of paramount importance in number theory, because of its relation to the distribution of prime numbers.
		The Gamma function along an interval In mathematics, the Gamma function is a function that extends the concept of factorial to the complex numbers.
	www.nationmaster.com /encyclopedia/Functional-equation (940 words)

	PlanetMath: functional equation of the Riemann zeta function (Site not responding. Last check: 2007-10-08)
		PlanetMath: functional equation of the Riemann zeta function
		"functional equation of the Riemann zeta function" is owned by mathcam.
		This is version 2 of functional equation of the Riemann zeta function, born on 2003-08-28, modified 2003-08-29.
	planetmath.org /encyclopedia/FunctionalEquationOfTheRiemannZetaFunction.html (97 words)

	equation - Article and Reference from OnPedia.com
		In mathematics, one often (not quite always) distinguishes between an identity, which is an assertion that two expressions are equal regardless of the values of any variables that occur within them, and an equation, which may be true for only some (or none) of the values of any such variables.
		In equations, the values of the variables for which the equation is true are called solutions.
		Thus to solve the equation, one must express those values of the variables that are solutions in terms of whatever constants may be included.
	www.onpedia.com /encyclopedia/equation (159 words)

	Functional equation (L-function) -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		Therefore use of the functional equation is basic, in order to study the zeta-function in the whole (Click link for more info and facts about complex plane) complex plane.
		A unified theory of such functional equations was given by (Click link for more info and facts about Erich Hecke) Erich Hecke, and the theory taken up again in Tate's thesis by (Click link for more info and facts about John Tate) John Tate.
		There are also functional equations for the (Click link for more info and facts about local zeta-function) local zeta-functions, arising at a fundamental level for the (analogue of) (Click link for more info and facts about Poincaré duality) Poincaré duality in (Click link for more info and facts about étale cohomology) étale cohomology.
	www.absoluteastronomy.com /encyclopedia/F/Fu/Functional_equation_(L-function)1.htm (617 words)

	Giulio M. Occhionero: The Functional Equation Headquarter
		While a function is an object of a certain variable which gives as result a value a functional is an object that has functions as variables and gives functions as results.
		Functionals can be generally expresses in integral form which is a technique to make them fall onto the ground of integral operators and eigenfunctions.
		Functional equations are equations where the unknown, a function, has to be found.
	www.occhionero.info /fueqhe.htm (447 words)

	Functional biography .ms (Site not responding. Last check: 2007-10-08)
		In such equations there may be several sets of variable unknowns, as when it is said that an additive function f is one satisfying the functional equation
		While in the foundational period of functional analysis from 1900-1920, it was largely the study of vector spaces such as the Lp spaces that are function spaces, the later axiomatic approach made no such assumption.
		The name linear functional, however, was carried over and applied to the dual space construction, in the general case.
	functional.biography.ms (352 words)

	WORMS Virtual Encyclopedia
		, that is an equation with an unknown function.
		Sometime it is easy to solve the functional equation, sometime it is difficult, and sometime it is impossible.
		It is intendent to stress the fact that the functional equation of DP does not have to be algebraic or numeric in natrure.
	www.worms.ms.unimelb.edu.au /encyclopedia/topics/dp.html (2296 words)

	Encyclopedia: Functional equation (L-function) (Site not responding. Last check: 2007-10-08)
		For example, the Riemann zeta-function has a functional equation relating its value at the complex number s with its value at 1 − s.
		The functional equation in question for the Riemann zeta-function takes the simple form
		Just the same shape of functional equation holds for the Dedekind zeta-function of a number field K, with an appropriate gamma-factor that depends only the embeddings of K (in algebraic terms, on the tensor product of K with the real field).
	www.nationmaster.com /encyclopedia/Functional-equation-%28L_function%29 (605 words)

	[No title]
		These functional equations are enough to compute Li2(z) anywhere in the complex plane (principal branch), by bringing z inside the unit circle and using the power series.
		Manipulation of the functional equations allows closed-form values to be determined for Li2 at z = 1, -1, 1/2, and 1/phi and 1/phi^2, where phi = 1.618...
		All simpler modular operations and functions, up through discrete logs, can be derived from analogies with the integer and real number versions of the functions, and can ultimately be traced back to counting operations.
	www.cs.arizona.edu /~rcs/dilog-paper-020402 (1754 words)

	Body
		This is not the case for the extended zeta or f function of equation (3).
		Equations (14) are conditionally convergent infinite series which, depending from the rearrangement of terms, can be divergent or convergent to some number including zero.
		Formally, since A(s) in functional equation (10) is determinate at all points of the critical strip including when x=1/2, f(s) and f(1-s) are different functions at all points of the critical strip except when x=1/2 and sin(ylnn)=0 for which f(s)=f(1-s)=0.
	www.coolissues.com /mathematics/Zeta/zeta.htm (1150 words)

	PlanetMath: example of solving a functional equation (Site not responding. Last check: 2007-10-08)
		According to the oddness one obtains for the general solution the sine function
		"example of solving a functional equation" is owned by pahio.
		This is version 9 of example of solving a functional equation, born on 2005-09-06, modified 2005-09-09.
	planetmath.org /encyclopedia/ExampleOnSolvingAFunctionalEquation.html (172 words)

	Ciencia Abierta Nº6
		As a matter of fact this last function has been widely used to explain the probabilistic distribution of said stresses in a large collection of materials and in diverse strain-states[3-8].
		The functional equation (1) is based on the hypothesis of the independence of the cumulative probabilities of non-fracture.
		The distribution function of cumulative probability defined by equation (32) is a Weibull statistics when the volume of the material, or the stress applied thereto, is approaching the value zero, as can be seen when equation (27) is expanded in Taylor series.
	cabierta.uchile.cl /revista/6/unicity.htm (1167 words)

	CHAPTER IX (Site not responding. Last check: 2007-10-08)
		CHAPTER IX The number of essentially different types of functions with which we have been concerned in the foregoing chapters is not very large, the most important being polynomials, rational, algebraic, explicit or implicit and trigonometric, direct or inverse functions.
		These new functions have generally been introduced, because it appeared that some problem which was occupying the attention of mathematicians was incapable of solution by means of the functions already known.
		Thus, the derivative of the exponential function is equal to the function itself.
	kr.cs.ait.ac.th /~radok/math/mat/chap9.htm (3470 words)

	Equation Article, Equation Information (Site not responding. Last check: 2007-10-08)
		In mathematics, one often (not quite always) distinguishes between anidentity, which is an assertion that two expressions are equal regardless of the values of any variables thatoccur within them, and an equation, which may be true for only some (or none) of the values of any such variables.
		In equations, the values of the variables for which the equation istrue are called solutions.
		Thus to solve the equation, one must express those values of the variables that are solutions in terms of whateverconstants may be included.
	www.anoca.org /variables/equations/equation.html (231 words)

	Abstracts
		Functional equations have many interesting applications in the characterization problems of probability theory (e.g.
		However, the arbitrariness in choosing the aggregating means leads to a non-compatibility of two ways of determining the national index, first one consisting in aggregating subindices on the national scale, and the other in counting regional indices first, and then accumulating them into a national index.
		The main goal of this work is to call attention to hypergroups and to the possibility of studying functional equations on hypergroups.
	www.math.klte.hu /analizis/conferences/debkat/2001/abstracts.html (1213 words)

	The functional equation of Riemann's zeta function (Site not responding. Last check: 2007-10-08)
		the functional equation of the Riemann zeta function
		In a recent lecture, Marek Wolf stated that the functional equation "is analogous to the Kramers-Wannier duality for the partition function of the two dimensional Ising model with parameter J expressed in units of kT (i.e.
		This counterpart to Poisson's summation formula is shown to be essentially 'equivalent' to the famous functional equation of Riemann's zeta-function, to the 'modular relation' of the theta-function, to the Nielsen-Doetsch summation formula for Bessel functions and to the partial fraction expansion of the periodic Hilbert kernel."
	www.maths.ex.ac.uk /~mwatkins/zeta/fnleqn.htm (987 words)

	Equation (Site not responding. Last check: 2007-10-08)
		Although the basic theory of structural equation modeling is an extension of single- equation regression concepts, the matrix language that is typically...
		Structural equation analysis is one of the most widely used...
		A multivariate logistic regression equation to screen for diabetes: development and validation.
	hallencyclopedia.com /Equation (447 words)

	Harald Fripertinger's Homepage -- Generalizations of the functional equation of the mean sun (Site not responding. Last check: 2007-10-08)
		Generalizations of the functional equation of the mean sun
		in A) of the functional equation of the mean sun are studied, where (A,+) is an Abelian group, K is a field, n is a positive integer, and both y:A
		(k) in the second case) are unknown functions, which will be determined by the equation.
	webdb.uni-graz.at /~fripert/reichsonne.html (93 words)

	Prace nagrodzone (Site not responding. Last check: 2007-10-08)
		Marek Kuczma, An introduction to the theory of functional equations and inequalities.
		Zbigniew Gajda, A characterization of functions with dense graph in the plane or half-plane, Ann.
		Boles³aw Gawe³, A linear functional equation and its dynamics, in: European conference on iteration theory, Batschuns, Austria, 10-16 September 1989, edited by Ch.
	ux1.math.us.edu.pl /mkuczma/prace.html (1458 words)

	Functional equation -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		The capital Γ denotes the (Click link for more info and facts about gamma function) gamma function.
		A simple form of functional equation is a (Click link for more info and facts about recurrence relation) recurrence relation.
		This, formally speaking, involves an unknown function on (Any of the natural numbers (positive or negative) or zero) integers, and also (Click link for more info and facts about translation operator) translation operators.
	www.absoluteastronomy.com /encyclopedia/f/fu/functional_equation.htm (430 words)

	Some thoughts on differential equation notation - functional vs classical
		a function, the composition of f and g (ie, f is called on the result of g called on the argument to the new function).
		This can then corrupt the associated reasoning (ie, there are allegedly a number of derivations of Hamilton's equations, which contain a step asserting "and now we consider the momentum to be independent of the velocities", an obvious absurdity, apparently motivated by notational opacity).
		In english, it is the rate of change in the values f gives (f's arguments having been provided by g and h from their arguments), in the neighborhood specified by those same arguments, as one of those arguments (x) varies.
	www.vendian.org /mncharity/dir3/dxdoc (1291 words)

	publications.html
		P.K. Sahoo, On a generalization of a functional equation associated with the distance between the probability distributions, Publicationes Mathematicae Debrecen, Tomos 46.
		P.K. Sahoo, On Two functional equations connected with the characterization of the distance measures, Aequationes Mathematicae, 54 (1997), 242-263.
		P.K. Sahoo and M. Sablik, On a functional equation in actuarial mathematics, Journal of Mathematical Analysis and its Applications, 253 (2001) 16-34.
	www.math.louisville.edu /~t0ried01/publ.html (469 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Right side of a table: virtual plotter drawing a graph for a mathematical equation Used mathematical equation is the spiral of Cornu.
		Functional block model for x coordinate using JavaScript EMBED Equation.3 Functional block model for y coordinate using JavaScript EMBED Equation.3 Aesthetics We implemented all 3D objects designed by our team members except for a clock 3d object which came from 3D café site (http://www.3dcafe.com/asp/default.asp).
		We used a functional block model to describe each step of the mathematical equation and simulated it using JavaScript.
	www.cise.ufl.edu /~fishwick/rube/worlds/plotter/Team_4.doc (609 words)

	Shades of the Cauchy functional equation \\ and Segre functions
		Shades of the Cauchy functional equation \\ and Segre functions
		This is a re-creation of a talk given at the 37th International Symposium on Functional Equations, May 18, 1999 (during Functional Equations Week in Huntington, West Virginia), at Marshall University.
		M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, Pa\'nstwowe Wydawnictwo Naukowe, 1985.
	www.lsus.edu /sc/math/rmabry/shades/ISFE37plus.htm (2014 words)

Try your search on: Qwika (all wikis)