Weierstrass M-Test

Let sum_(n=1)^(infty)u_n(x) be a series of functions all defined for a set E of values of x. If there is a convergent series of constants


such that


for all x in E, then the series exhibits absolute convergence for each x in E as well as uniform convergence in E.

See also

Absolute Convergence, Uniform Convergence

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Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 301-303, 1985.Jeffreys, H. and Jeffreys, B. S. "M Test" and "Extension of the M 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.

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Weierstrass M-Test

Cite this as:

Weisstein, Eric W. "Weierstrass M-Test." From MathWorld--A Wolfram Web Resource.

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