Weierstrass M-test

The Weierstrass M-test is a mathematical tool used in analysis to determine the uniform convergence of an infinite series of functions. Developed by Karl Weierstrass, a pioneering mathematician in the theory of functions, this test provides a rigorous method for establishing convergence.

The test states that if for each function in a series, there exists a constant M such that the absolute value of the function is less than or equal to M, and the sum of these constants converges, then the original series of functions converges uniformly. This is crucial because uniform convergence ensures that properties like continuity are preserved when dealing with sequences and series of functions.12