
	Where results make sense

Topic: Power series method

Related Topics

Frobenius method

Ordinary differential equation

Analytic function

Proof that holomorphic functions are analytic

Frobenius theorem

Georg Frobenius

Wilmot Township, Pennsylvania

In the News (Mon 21 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Power series correction in a linear fiber optic analog transmission system and method - US Patent 5528405 (Site not responding. Last check: 2007-10-08)
		The method of claim 1 further comprising the step of filtering the guard band with a notch filter to reduce energy in the notch-filtered section before the information signals are transmitted, and wherein the guard band measured energy represented by the second power series is the energy in the notch-filtered section.
		The method of claim 2 wherein the guard band is filtered with plural of the notch filters, and wherein the guard band measured energy represented by the second power series is related to the energy in the plural notch-filtered sections.
		The present invention relates to systems and methods for improving the linearity of an analog transmission, and more particularly to a system and method in which a power series correction is applied to a transmission received on a fiber optic cable to reduce non-linearities in the received transmission.
	www.patentstorm.us /patents/5528405.html (2219 words)

	Method and apparatus for power series training using a change-variable - US Patent 6542877 (Site not responding. Last check: 2007-10-08)
		A method is provided for calculating the change in level which is output from a multivariable power series as a separate variable, where this change out put signal is the change in level which is output when supply input is from two different data points.
		The method of calculating the change output as a separate signal is generalized so that the derivative of all parameters used in the construction of the multivariable power series can be calculated with the change output signal.
		The power series built using the variable with the highest index will be built using the values returned from calls to the same procedure called with a control integer one less than that used to build the power series with the highest index.
	www.patentstorm.us /patents/6542877.html (7766 words)

	Power series method - Wikipedia, the free encyclopedia
		In mathematics, the power series method is used to seek a power series solution to certain differential equations.
		The power series method tells us we may be able to construct a power series solution
		which can be further simplified by the use of hypergeometric series (which goes beyond the scope of this article).
	en.wikipedia.org /wiki/Power_series_method (178 words)

	306chX.html
		The goal of the power series method is to determine the coefficients a[n],n=0,1,2,...
		The recurrence equations are found by substituting the power series for y into the DE and equating the coefficients of the different powers of t.
		Although the strength of the power series method is the ability to solve differential equations with variable coefficients, the method can also be applied to d.e.'s with constant coefficients such as the harmonic equation.
	www.math.buffalo.edu /306/306chX1.html (848 words)

	Convergence of Power series (Site not responding. Last check: 2007-10-08)
		Improvement of the convergence of a planetary potential expansion - The method o...
		Abstract - Convergence of a power series used in Seismic Processing...
		On the convergence of the power series algorithm...
	www.scienceoxygen.com /math/450.html (148 words)

	PlanetMath: formal power series (Site not responding. Last check: 2007-10-08)
		Formal power series allow one to employ much of the analytical machinery of power series in settings which don't have natural notions of convergence.
		It is also possible to define partial derivatives for formal power series in a straightforward way.
		This is version 8 of formal power series, born on 2002-07-01, modified 2005-02-13.
	planetmath.org /encyclopedia/GeneratingFunction.html (762 words)

	Encyclopedia: Power series method
		In mathematics, a power series (in one variable) is an infinite series of the form where the coefficients an, the center c, and the argument x are usually real or complex numbers.
		In mathematics, an analytic function is a function that is locally given by a convergent power series.
		In mathematics, a hypergeometric series is the sum of a sequence of terms in which the ratios of successive coefficients k is a rational function of k.
	www.nationmaster.com /encyclopedia/Power-series-method (363 words)

	Power series expansions (Site not responding. Last check: 2007-10-08)
		A useful method for obtaining solutions in a general case is based on the use of power series expansions.
		Such solutions are often used in combination with numerical techniques: A power series solution is used to provide initial values for the numerical integration.
		When we use the power series method to solve differential equation we will frequently need to use this trick, and it is important that we understand it.
	www.maths.soton.ac.uk /staff/Andersson/MA273/node30.html (343 words)

	Evaluation of a power series (Site not responding. Last check: 2007-10-08)
		A power series is a summation, from i=0 to i=n, of ai x^i where x is a complex variable.
		The radius of convergence r is the distance to the closest singularity of the function represented by the infinite power series.
		Usually, the power series is obtained as the Taylor series of the function, about the point p.
	www.rism.com /Trig/evaluati.htm (221 words)

	Department of Mathematics and Computer Science Official Syllabus (Site not responding. Last check: 2007-10-08)
		Solve ordinary differential equations by the power series method and the method of Frobenius.
		Use Fourier series methods to solve the one-dimensional heat equation on a finite domain.
		Methods of Instruction: The methods of instruction are determined by the instructor; however, the instructor is expected to use a variety of methods.
	radar.ngcsu.edu /~egreen/4900f03.htm (438 words)

	Formal power series -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		They are also useful to compactly describe (Serial arrangement in which things follow in logical order or a recurrent pattern) sequences and to find closed formulas for (Click link for more info and facts about recursively) recursively defined sequences; this is known as the method of generating functions and will be illustrated below.
		The addition and multiplication of such sums follow the usual laws of power series.
		Formal power series can also be interpreted as functions, but one has to be careful with the (Territory over which rule or control is exercised) domain and (Click link for more info and facts about codomain) codomain.
	www.absoluteastronomy.com /encyclopedia/f/fo/formal_power_series.htm (1908 words)

	PASS 2002 - Power Analysis and Sample Size Software. Design of Experiments. Experimental Design. Scientific Studies. N.
		A statistical test's power is the probability that the test procedure will result in statistical significance.
		Power is related to the sample size, the size of the type 1 (alpha) error, the actual size of the effect, and the size of experimental error.
		As statistical significance is usually the desired outcome, planning and running a study to achieve a high power is of prime importance to the researcher.
	www.ncss.com /pass.html (559 words)

	Frobenius method - Wikipedia, the free encyclopedia
		In mathematics, the Frobenius method describes a way to find an infinite series solution for a second-order ordinary differential equation of the form
		The Frobenius method enables us to create a power series solution to such a differential equation.
		is a rational function, the power series can be written as a hypergeometric series.
	www.wikipedia.org /wiki/Frobenius_method (331 words)

	Series-connected microwave power amplifiers with voltage feedback and method of operation for the same - Patent 5945879
		The limitations to such "corporate" power combining networks are similar to those of impedance matching networks for microwave power amplifier designs, namely as the level of power combining is increased, the physical size of the power combiners increases, their skin effect losses increase, and the feasible system bandwidth decreases.
		The innovation introduced by the present invention is a method of distributing the total output voltage equally between the transistors in the series, despite the presence of serious transistor parasitics.
		Class B operation is a standard microwave power amplifier operation mode where the standby current and hence the power consumed by the transistor is zero with currents drawn in the drain only when signal to be amplified is applied at the input.
	www.freepatentsonline.com /5945879.html (5971 words)

	Summability of Power Series Solutions of q-Difference Equations
		Like differential equations, q-difference equations may have divergent power series solutions and the aim is to develop a theory of summability for such series like it has been done by Martinet-Ramis and Écalle for solutions of differential equations.
		When there is the slope 0 and a non zero slope then the origin 0 is an irregular singular point; the number of solutions without an exponential factor is equal to the length of the zero slope.
		Proposition 2 q-summable series of level k are naturally given a structure of C{x}-module, not a structure of algebra.
	algo.inria.fr /seminars/sem97-98/zhang.html (1048 words)

	AVault \| PC \| Call to Power II Review (Site not responding. Last check: 2007-10-08)
		Your goal in Call to Power II is the construction of a great empire that will evolve throughout the ages to face a destiny filled with urban warfare and nanotechnological threats.
		The second method is based on your score as a leader assuming you survive the full timeline up to 2300 AD: your score will be based on the number of accomplishments you have made along with wonders, population, cities and other factors too numerous to list.
		Call to Power II continues in the same vein as its predecessor in that much of the micromanagement infrastructure has been removed, forcing you to take the reins on a much larger scale rather than worrying about the minute flow of resources in each city.
	www.avault.com /reviews/review_temp.asp?game=ctp2 (881 words)

	Power Series Applications (Site not responding. Last check: 2007-10-08)
		For Power Series, however, I know little of how they are applied in physics, engineering, and other fields.
		Rich Robinson ==================================================== Power series are infinite series that contain terms X^r, that is X raised to a series of exponents.
		There are some very elegant infinite series such as the power series expression called Fibonacci series (you can find a lot of books on these).
	www.newton.dep.anl.gov /askasci/math99/math99165.htm (469 words)

	Slitting: Theory
		This method of reducing the data and solving for stresses is very powerful.
		This technique was originally developed for the Hole Drilling method as the "Power Series" method of solving for residual stress [Schajer, G.S., "Application of Finite Element Calculations to Residual Stress Measurements," J. of Engineering Materials and Technology, V. 103, 1981, pp.
		The body force method has been used to calculate compliances for finite width slots simply and accurately - see the references section, refs 20 & 27, for examples.
	www.lanl.gov /projects/residual/theory.shtml (427 words)

	Differential Equations Lecture Notes, 11/13/03 (Site not responding. Last check: 2007-10-08)
		It is worthwhile at this time to review what you've learned about power series from Calculus.
		Substitute the power series we've constructed into the differential equation we are trying to solve, and now "equate coefficients" of like powers of x.
		After we've constructed our power series solution for y, be sure to determine the radius of convergence for the series, e.g.
	www.assumption.edu /Alfano/MAT355-FA03/Notes/111303.html (400 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		A Power Series is an expression of the form: a
		An Power Series is said to converge (to a Limit L - a function) if the Sequence of Partial Sums converges.
		, of a Power Series is the Limit of the Absolute Values of the ratio of consecutive terms, expressed in terms of the "counter" n.
	www.tam.cornell.edu /courses/310Sp97/L7Feb/Lec7Feb.htm (264 words)

	No Title
		The confirmations he achieved using his power series method justified in his mind the ultimate correctness of this procedure.
		Among the curves worked on by Newton were the Cartesian ovals, the Cissoid, the Conchoid, the Cycloid, the Epicycloid, the Epitrochoid, the Hypocycloid, the Hypotrochoid, the Kappa curve and the Serpentine.
		Thus he was able to derive simple and general methods compared with the laborious work of his contemporaries.
	www.math.tamu.edu /~don.allen/history/calc1/calc1.html (1395 words)

	Catalogue of GP/PARI Functions: Polynomials and power series
		The method used is a modified version of the round 4 algorithm of Zassenhaus.
		Every type is allowed for x, but if it is not a genuine polynomial (or power series, or rational function), the substitution will be done as if the scalar components were polynomials of degree one.
		If x is a power series, z must be either a polynomial, a power series, or a rational function.
	www.skalatan.de /pariguide/doc/Polynomials_and_power_series.html (1912 words)

	Power Series
		On the power series expansions for the sine and cosine
		Iterative roots of formal power series: universal expressions for the coefficients and analytic iteration.
		On a Criterion of Pringsheim's for Expansibility in Taylor's Series
	mathews.ecs.fullerton.edu /c2003/PowerSeriesBib/Links/PowerSeriesBib_lnk_3.html (851 words)

	8. (Site not responding. Last check: 2007-10-08)
		Hence, this theorem expressly requires that, after differentiating the series term by term, we must still investigate whether the result of the differentiation is a uniformly convergent series or not.
		Every function represented by a power series can be differentiated as often as we please within the interval of convergence and the differentiation can be performed term by term.
		The construction of such a theory of power series presents no difficulties once we have defined the concept of limit in the domain of complex numbers; in fact, it follows almost exactly the theory of real power series.
	kr.cs.ait.ac.th /~radok/math/mat6/calc81.htm (5917 words)

	MacintoshHD:Desktop Folder:310 Spring 97:CompProj4:comproj4.html (Site not responding. Last check: 2007-10-08)
		The Power Series Method is introduced and developed in Chapter 8 of the textbook.
		You should also analyze the errors committed using your series in place of the "exact" solution, i.e., give the user of the series solutions advice about how large a range of x the series is valid, for a given error.
		The Radius of Convergence of the two series is "infinity".
	www.tam.cornell.edu /courses/310Sp97/Projects/CompProj4/proj4.htm (553 words)

	Inverse Z-Transform (Site not responding. Last check: 2007-10-08)
		This "method" is to basically become familiar with the z-transform pair tables and then "reverse engineer".
		One of the advantages of the power series expansion method is that many functions encountered in engineering problems have their power series' tabulated.
		To further expand on this method of finding the inverse requires the knowledge of complex variable theory and thus will not be addressed in this module.
	cnx.rice.edu /content/m10651/latest (369 words)

	Series Solutions and Frobenius Method (Site not responding. Last check: 2007-10-08)
		Power series solutions around a singular point of the system of hypergeometric differential equations of type (3,6) by use of special values of 3F2.
		A necessary condition for a power series to be a formal solution of a singular linear differential equation of order k.
		Estimate of the radius of convergence of power series in a small parameter which represent periodic solutions of systems of differential equations.
	math.fullerton.edu /mathews/n2003/frobeniusdiffeqns/FrobeniusSeriesBib/Links/FrobeniusSeriesBib_lnk_3.html (2042 words)

	You can count on power series (Site not responding. Last check: 2007-10-08)
		You have seen that power series are useful for all kinds of calculus stuff: integration, limits, differential equations.
		But, as you may already know from comparing the series method with l'Hopital's method of calculating limits, there is one remarkable feature about power series, namely: The tougher the problem, the happier the power series.
		But it is still a feast to see how power series produce the answer, seemingly by miracle.
	www.math.utk.edu /~denzler/CalculusND/countpow.html (299 words)

	Objectives for Exam III (Site not responding. Last check: 2007-10-08)
		This is a list of keywords - the main themes/solution methods that will be covered in the test.
		Power series for sin, cos, exp, geometric series (3.1)
		Power series Method for (linear) equations with non-constant coefficients (3.1)
	www.public.iastate.edu /~roettger/267/ex3.html (162 words)

Try your search on: Qwika (all wikis)