ISSN:
1572-9265
Keywords:
41A21
;
30E10
;
Simultaneous rational approximant
;
q-hypergeometric series
;
convergence of Hermite-Padé approximants
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract We investigate the convergence of simultaneous Hermite-Padé approximants to then-tuple of power series $$f_i (z) = \sum\limits_{k = 0}^\infty {C_k^{(i)} z^k ,} i = 1,2,...,n,$$ where $$C_0^{(i)} = 1;C_k^{(i)} = \prod\limits_{p = 0}^{k - 1} {\frac{1}{{(C - q^{\gamma i + p} )}},} k \ge 1.$$ 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02141927
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