Convergence of simultaneous Hermite-Padé approximants to the n-tuple of q-hypergeometric series {2Φ0((A, αj), (1, 1); z)}jn=1

• Autores: M. G. de Bruin, K.A. Driver, D. S. Lubinsky
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Nº 1, 1993, pág. 37
• Idioma: inglés
• DOI: 10.1016/0377-0427(93)90132-u
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• Resumen

  • We investigate the convergence of simultaneous Hermite-Padé approximants for the n-tuple of power series fi(z)=∑∞k=0C(i)kzk,i=1,2,…,n, where C(i)0 = 1, C(i)k=∏k−1p=0(A−qαi+p), k ⩾ 1. Here A, qϵ ,αiϵ , i = 1,…,n. For ∥A∥ ≠ 1, if q = eiθ,θ ϵ(0, 2π) and θ/(2π) is irrational, each fi(z), i = 1,…,n, has a natural boundary on its circle of convergence. We show that certain sequences of Hermite-Padé approximants converge in capacity of (f1(z),…,fn(z)) inside the common circle of convergence of each fi, i = 1,…,n.