Weierstrass M-test

The Weierstrass M-test is a mathematical tool used to determine whether a series of functions converges uniformly. In simpler terms, if you have a series that adds up different functions, the M-test helps to confirm if they come together nicely as you include more terms. It requires finding a simple set of limits (M-values) for each function that ensures the overall series doesn’t behave erratically. If these conditions are met, it guarantees that the series will converge uniformly to a single function, making analysis and further calculations more manageable and reliable.