Abstract
We investigate the convergence of simultaneous Hermite-Padé approximants to then-tuple of power series
where
HereC, q∈ℂ, γ i ∈ℝ,i=1, 2,...,n. For |C|≠1, ifq=eiθ, θ∈(0, 2π) and θ/2π is irrational, eachf i (z),i=1,...,n, has a natural boundary on its circle of convergence. We show that “close-to-diagonal” and other sequences of Hermite-Padé approximants converge in capacity to (f 1(z),..., fn (z)) inside the common circle of convergence of eachf i (z),i=1,...,n.
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De Bruin, M.G., Driver, K.A. & Lubinsky, D.S. Convergence of simultaneous Hermite-Padé approximants to then-tuple ofq-hypergeometric series\(\{ {}_1\Phi _1 (_{(c,\gamma _j )}^{(1,1)} ;z)\} _{j = 1}^n \) . Numer Algor 3, 185–192 (1992). https://doi.org/10.1007/BF02141927
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DOI: https://doi.org/10.1007/BF02141927