Speed of convergence of quadratic Hermite–Padé approximations confluent hypergeometric functions

The speed of convergence (including non-diagonal) of quadratic Hermite–Padé approximations of the system of the second kind $\{_1F_1(1,\gamma;\lambda_jz)\}^2_{j=1}$ is found. It consists of two degenerate hypergeometric functions when $\{\lambda_j\}_{j=1}^2$ are arbitrary distinct complex numbers, and $\gamma\in\mathbb{C}\setminus\{0, -1, -2,\dots\}$. These proved theorems supplement and generalize the results obtained earlier by other authors.