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Topic: Radius of convergence


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In the News (Sun 21 Jul 19)

  
  PlanetMath: radius of convergence
smaller than the radius of convergence, the power series converges uniformly within the closed disk of radius
Cross-references: closed, converges uniformly, radius, limit, complex number, diverges, complex, real, converges absolutely, series, power series
This is version 8 of radius of convergence, born on 2002-03-19, modified 2007-03-02.
planetmath.org /encyclopedia/RadiusOfConvergence.html   (128 words)

  
  Radius of convergence - Wikipedia, the free encyclopedia
The radius of convergence is infinite if the series converges for all complex numbers z.
The radius of convergence can be found by applying the root test to the terms of the series.
The radius of convergence is always equal to the distance from the center to the nearest point where the function f has a (non-removable) singularity; if no such point exists then the radius of convergence is infinite.
en.wikipedia.org /wiki/Radius_of_convergence   (727 words)

  
 Power Series and the Radius of Convergence
Definition 7.5 The number R described above is called the radius of convergence of the power series.
It is characterised by the fact that the series converges (absolutely) inside this interval and diverges outside the interval.
The word ``radius'' is used, because in fact the same result is true for complex series, and then we have a genuine circle of convergence, with convergence for all (complex) z with
www.maths.abdn.ac.uk /~igc/tch/ma2001/notes/node54.html   (739 words)

  
 Radius of Convergence
The number R is called the radius of convergence.
The set of all values of x for which the power series converges is called the interval of convergence of the power series.
The radius of convergence is 0 and the interval of
www.mecca.org /~halfacre/MATH/radiusofconv.htm   (253 words)

  
 The Radius of Convergence etc.
In our example, the center of the power series is 0, the interval of convergence is the interval from -1 to 1 (note the vagueness about the end points of the interval), its length is 2, so the radius of convergence equals 1.
Thus the interval of convergence is the interval
The interval of convergence is the interval from
www.sosmath.com /calculus/radcon/radcon02/radcon02.html   (513 words)

  
 The Radius of Convergence of Series Solutions
The natural questions arise, for which values of t these series converge, and for which values of t these series solve the differential equation.
The first question could be answered by finding the radius of convergence of the power series, but it turns out that there is an elegant Theorem, due to Lazarus Fuchs (1833-1902), which solves both of these questions simultaneously.
In other words, the radius of convergence of the series solution is at least as big as the minimum of the radii of convergence of p(t) and q(t).
www.sosmath.com /diffeq/series/series05/series05.html   (469 words)

  
 Calculus II (Math 2414) - Series & Sequences - Power Series   (Site not responding. Last check: 2007-10-19)
The way to determine convergence at these points is to simply plug them into the original power series and see if the series converges or diverges using any test necessary.
In the previous example the power series didn’t converge for either end point of the interval.  Sometimes that will happen, but don’t always expect that to happen.  The power series could converge at either both of the end points or only one of the end points.
The radius of convergence is NOT 3 however.  The radius of convergence requires an exponent of 1 on the x.  Therefore,
tutorial.math.lamar.edu /AllBrowsers/2414/PowerSeries.asp   (1394 words)

  
 Mathwords: Radius of Convergence
The distance between the center of a power series' interval of convergence and its endpoints.
If the series only converges at a single point, the radius of convergence is 0.
If the series converges over all real numbers, the radius of convergence is ∞.
www.mathwords.com /r/radius_of_convergence.htm   (63 words)

  
 Existence of radius of convergence   (Site not responding. Last check: 2007-10-19)
to the edge of this interval is called the radius of convergence.
We think of the radius of convergence being infinite in this case.
We would say that the radius of convergence here is 0 and there are no endpoints to consider.
math.la.asu.edu /~jj/271/ratio/node3.html   (213 words)

  
 Radius of convergence   (Site not responding. Last check: 2007-10-19)
Why is the radius of convergence of the first 6 terms of the power series expansion of x^(1/2) centered at 4 less than 6?
centered at 4, if r is the radius of convergence then for any x which is less than r units from 4, ie.
Thus the radius of convergence of the power series is less than of equal to 4 and hence less than 6.
mathcentral.uregina.ca /QQ/database/QQ.09.98/stave1.html   (135 words)

  
 Convergence Communications   (Site not responding. Last check: 2007-10-19)
However when Horn heard about a real-time communications solution that was used to manage security when President George Bush and Senator John Kerry met for the second presidential debate at Washington University in St. Louis, Missouri she decided to investigate.
It didn't take long for senio r officers at the Jacksonville Sheriff 's Office to buy into the solution and by January 2005, Convergence Communications was busy configuring the system to meet the standards of the National Incident Management System model and accommodate the special needs of the Super Bowl's designated lead security agency.
Online registration utilizing a customized process built by Convergence was quick and easy, and by the time the Sheriff 's Office had finished ratifying applicants' credentials the number of authenticated participants on the system reached 650.
www.convergencecom.com /casestudy_techatsuperbowl.shtml   (2751 words)

  
 Radius of convergence when integrating and differentiating power series   (Site not responding. Last check: 2007-10-19)
Radius of convergence when integrating and differentiating power series
The radius of convergence remains the same under either operation.
Thus the radius of convergence is the same as it was for the original series.
math.la.asu.edu /~jj/271/ratio/node4.html   (157 words)

  
 What is the Radius of Convergence?
The radius of convergence for this function is one.
The convergence of the infinite series at X=-1 is spoiled because of a problem far away at X=1, which happens to be at the same distance from zero!
The radius of convergence is usually the distance to the nearest point where the function blows up or gets weird.
www.lassp.cornell.edu /sethna/Cracks/What_Is_Radius_of_Convergence.html   (463 words)

  
 MRWmath (12): Mathematical ASCII Notation - Apronus.com
Show that it is the radius of convergence of the power series a[n]*z^n.
^ (1/n) is the radius of convergence of the power series a[n]*z^n.
Hence the radius must be at least 1.
www.apronus.com /math/mathascii99/mathascii12.htm   (344 words)

  
 Radius of Convergence   (Site not responding. Last check: 2007-10-19)
Call the number R of the theorem the radius of convergence.
The domain of convergence of the series must be one of:
has radius of convergence R = 5 and domain of convergence D
pear.math.pitt.edu /Calculus2/week13/13_2li6.html   (94 words)

  
 Securing a RADIUS server - Network World
The RADIUS server (and its data store or authentication backend) is what controls access to the network and additionally supplies the keys used by the AP and wireless client to encrypt a given station's traffic.
This limits the exposure of the RADIUS server and insures that vulnerabilities in other services running on the system do not lead to the RADIUS server being compromised.
In order to operate, the RADIUS server needs to be able to communicate with your authentication backend (e.g., an LDAP or SQL server) and each of your Network Access Servers (NAS), which in the case of a wireless network are your APs.
www.networkworld.com /columnists/2007/050707-wireless-security.html   (1140 words)

  
 Radius of Convergence
is called the radius of convergence of the power series.
Inside its radius of convergence a power series is absolutely convergent and has a little wiggle room before you get outside the radius of convergence.
It is possible for L=0 in which case we will get convergence for all x.
www.iwu.edu /~lstout/series/node6.html   (154 words)

  
 Radius of convergence   (Site not responding. Last check: 2007-10-19)
In using a power series expansion we clearly need to worry about convergence.
If we need to include a huge number of terms, the expansion is not very useful.
and the series converges only at the centre (which is quite useless).
www.soton.ac.uk /~jhr/MA273/node31.html   (83 words)

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