Let 
be a series of functions all defined for a set 
of values of 
. If there is a convergent series
of constants
 |
such that
 |
for all 
,
then the series exhibits absolute convergence
for each 
as well as uniform convergence in 
.
Weierstrass M-Test
See also
Absolute Convergence, Uniform ConvergenceExplore with Wolfram|Alpha
References
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 301-303, 1985.Jeffreys, H. and Jeffreys, B. S. "
Test" and "Extension of the 
Test." §1.1151-1.1152 in Methods
of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University
Press, pp. 40-41, 1988.Knopp, K. Theory
of Functions Parts I and II, Two Volumes Bound as One, Part I. New York:
Dover, p. 73, 1996.Referenced on Wolfram|Alpha
Weierstrass M-TestCite this as:
Weisstein, Eric W. "Weierstrass M-Test." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WeierstrassM-Test.html