ZEROS OF PADE APPROXIMANTS FOR ENTIRE-FUNCTIONS WITH SMOOTH MACLAURIN COEFFICIENTS

For entire functions f(z) = SIGMA(j=0)infinitya(j)z(j) whose coefficients satisfy the smoothness condition a(j) + 1a(j-1)/a(j)2 --> eta as j --> infinity we investigate the asymptotic behavior as n --> infinity of the normalized partial sums s(n)(za(n)/a(n+1) and the normalized Pade numerators P(n,m)(za(n)/a(n+1), m fixed. As a consequence we deduce results on the limiting behavior of the zeros of these polynomials. (C) 1994 Academic Press, Inc.