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

  • N.P. Hoyenko Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, Ukraine
  • V.R. Hladun Lviv Polytechnic National University, 12 Bandera str., 79013, Lviv, Ukraine
  • O.S. Manzij Lviv Polytechnic National University, 12 Bandera str., 79013, Lviv, Ukraine
Keywords: Appell hypergeometric function, branched continued fraction
Published online: 2014-07-19

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.

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