Generalization of Jamet's test for convergence of number series and its new modifications

TL;DR

This paper introduces new generalized logarithmic convergence tests for number series, extending Jamet's and Schlomilch's tests, and proposes modified convergence tests based on these generalizations.

Contribution

It presents novel generalizations of existing convergence tests and derives new modified tests for number series, expanding the analytical tools available.

Findings

New generalized logarithmic convergence tests introduced

Derived modified convergence tests based on generalizations

Enhanced criteria for convergence of number series

Abstract

In this article, we present new generalizations of logarithmic convergence tests for number series, from which we will derive various new generalizations of the Jamet's convergence test. Further, similarly, on the basis of the generalizations of the Schlomilch's test we found, we will obtain modified tests of the convergence of number series.