On the infinite remains of the Nörlund branched continued fraction for Appell hypergeometric functions

Abstract

The correspondence, convergence and stability to perturbations of the infinite remains of the Nörlund branched continued fraction are investigated in a poly-disc $\{ (z_1,z_2)\in \mathbb{C}^2: |z_j|\leq r, j=1,2\}$, $0<r<1/8$, in case of arbitrary parameters of Appell hypergeometric function.