Gauss Test and Logarithmic Test for the Determination of Uniform Convergence of Function Series

Based on the idea of extending the convergence test for series of positive terms to the uniform convergence of function series, an analogy was made between the Gauss test, Logarithmic test, and Quasi- Logarithmic test and their limiting forms and thus worked out the corresponding test for determining the uniform convergence of function series, which helps enrich the uniform convergence of function series.