Abel's Uniform Convergence Test

Let be a Sequence of functions. If

1. can be written ,

2. is Convergent,

3. is a Monotonic Decreasing Sequence (i.e., )for all , and

4. is Bounded in some region (i.e., for all )

then, for all , the Series Converges Uniformly.

References

Bromwich, T. J. I'a and MacRobert, T. M. An Introduction to the Theory of Infinite Series, 3rd ed. New York: Chelsea, p. 59, 1991.

Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, p. 17, 1990.

• Tait Flyping Conjecture
• Tait's Hamiltonian Graph Conjecture
• Tait's Knot Conjectures
• Takagi Fractal Curve
• Take-Away Game
• Takeuchi Function
• TAK Function
• Talbot's Curve
• Talisman Hexagon
• Talisman Square
• Tame Algebra
• Tame Knot
• Tangency Theorem
• Tangent
• Tangent Bifurcation
• Tangent Bundle
• Tangent Developable
• Tangent Hyperbolas Method
• Tangential Angle
• Tangential Triangle
• Tangential Triangle Circumcenter
• Tangent Indicatrix
• Tangent Line
• Tangent Map
• Tangent Number