Absolute monotonicity of normalized remainders involving the Gauss hypergeometric functions and complete elliptic integrals of the second kind

In the paper, the authors concisely prove the absolute monotonicity of two functions and their normalized remainders involving the Gauss hypergeometric functions and complete elliptic integrals of the second kind. These arguments are different from the corresponding discussions in the paper “F. Wang and F. Qi, Absolute monotonicity of four functions involving the second kind of complete elliptic integrals , J. Math. Inequal. 19 (2025), no. 2, 605–624. DOI: https://doi.org/10.7153/jmi-2025-19-37 ”.