SIMULTANEOUS RATIONAL APPROXIMANTS FOR A PAIR OF FUNCTIONS WITH SMOOTH MACLAURIN SERIES COEFFICIENTS

[摘要] Let f(z) = Sigma(j = 0)(infinity) and g(z) = Sigma(j = 0)(infinity) be formal power series for which the quantities a(j + 1)a(j - 1)/a(j)(2) and (b(j)/b(j + 1))/(a(j)/a(j + 1)) have a prescribed asymptotic behaviour as j --> infinity. We obtain the asymptotic behaviour as l --> infinity of the (l - s, r, s), l, r, s is an element of N, Hennite-Pade approximant to (f, g) and the associated determinants. (C) 1995 Academic Press. Inc.

[发布日期] 1995-12-01