CONVERGENCE OF SIMULTANEOUS HERMITE-PADE APPROXIMANTS TO THE N-TUPLE OF Q-HYPERGEOMETRIC SERIES ((2)PHI(0)((A,ALPHA(J)), (1,1) Z))(J=1)(N)

[摘要] We investigate the convergence of simultaneous Hermite-Pade approximants for the n-tuple of power series f(i)(z) = SIGMA(k=0)(infinity)C(k)(i)z(k), i = 1, 2,..., n, where C0(i) = 1, C(k)(i) = PI(p=0)k-1(A - q(alpha(i) + p)), k less-than-or-equal-to 1. Here A, q is-an-element-of C, alpha(i) is-an-element-of R, i = 1, ..., n. For Absolute value of A not-equal 1, if q = e(itheta), theta is-an-element-of (0, 2pi) and theta/2(pi) is irrational, each f(i)(z), i = 1, ..., n, has a natural boundary on its circle of convergence. We show that certain sequences of Hermite-Pade approximants converge in capacity to (f1(z),..., f(n)(z)) inside the common circle of convergence of each f(i), i = 1,..., n.

[发布日期] 1993-12-31

[效力级别]  Proceedings Paper

[关键词] HERMITE-PADE APPROXIMANT;CONVERGENCE;Q-HYPERGEOMETRIC SERIES