Uniform Convergence
A Series 
is uniformly convergent to 
for a set 
of values of 
if, for each
, an Integer 
can be found such that
 | (1) |
and all 
. To test for uniform convergence, use Abel's Uniform Convergence Test or theWeierstraß M-Test. If individual terms 
of a uniformly converging series arecontinuous, then- 1. The series sumis continuous,
(2) - 2. The series may be integrated term by termand
(3) - 3. The series may be differentiated term by term
(4)
References
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 299-301, 1985.
- Perspective
- Perspective Axis
- Perspective Center
- Perspective Collineation
- Perspective Triangles
- Perspectivity
- Pesin Theory
- Petersen Graphs
- Petersen-Shoute Theorem
- Peters Projection
- Peter-Weyl Theorem
- Petrie Polygon
- Petrov Notation
- Pfaffian Form
- p-Good Path
- p-Group
- Phase
- Phase Space
- Phase Transition
- Phasor
- Phi Curve
- Phi Number System
- Phragmén-Lindêlöf Theorem
- Phyllotaxis
- Pi