made with Mathematica technology MathWorld
Algebra
Applied Mathematics
Calculus and Analysis
Discrete Mathematics
Foundations of Mathematics
Geometry
History and Terminology
Number Theory
Probability and Statistics
Recreational Mathematics
Topology
Alphabetical Index
Interactive Entries
Random Entry
New in MathWorld
MathWorld Classroom
About MathWorld
Contribute to MathWorld
Send a Message to the Team
MathWorld Book
12,905 entries
Last updated: Mon Jan 5 2009

Created, developed, and nurtured by Eric Weisstein
at Wolfram Research
Calculus and Analysis > Series > Convergence >

Cauchy-Hadamard Theorem

The radius of convergence of the Taylor series

a_0+a_1z+a_2z^2+...

is

r=1/(lim_(n->infty)^_(|a_n|)^(1/n)).

SEE ALSO: Radius of Convergence, Taylor Series




CITE THIS AS:

Weisstein, Eric W. "Cauchy-Hadamard Theorem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Cauchy-HadamardTheorem.html

SendContact the MathWorld Team
© 1999-2009 Wolfram Research, Inc. | Terms of Use

The Wolfram Demonstrations Project Browse Topics View Latest
JUST RELEASED: Wolfram Mathematica 7
 Other Wolfram Web Resources »
Wolfram Research
Mathematica Home Page
Mathematica Documentation Center
Wolfram Demonstrations Project
Online Integrator
Functions Site
Wolfram Tones
Wolfram Science
Wolfram Blog
more…