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A method to test the uniform convergence of function series
- 1 Lanzhou University
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Abstract
The series refer to performing infinite addition operations on infinite numbers or functions in a certain order. It is hard to find out whether the positive function series converges uniformly in many cases. In this article, a new method that replacing the sum of function terms series with improper integral will be introduced, which is designed to solve problems that cannot be solved by classical Weierstrass M-test. The Cauchy uniform convergence test will serve as the basis for the entire proof process because it can lead the focus point from the whole sum to the partial sum of the function series, where its value can be easier substituting by the value of the improper integral. After using basic knowledge of the improper integral, the uniform convergence can finally be known. By using this method, testing the uniform convergence of the irregular function series even estimating its value can be possible accomplished.
Keywords
Uniform convergence of function series, Improper integral, Cauchy’s convergence test, Weierstrass M-test, Mathematical analysis
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Cite this article
Wu,Z. (2024). A method to test the uniform convergence of function series. Theoretical and Natural Science,41,6-9.
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Volume title: Proceedings of the 2nd International Conference on Mathematical Physics and Computational Simulation
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