On the Eneström-Kakeya Theorem

A classical result of Eneström and Kakeya (If an ≥ an−1 ≥ ••• ≥ a0 > 0, then, for |z| > 1, ∑nk=0akzk ≠ 0) is extended to polynomials whose coefficients satisfy the condition tnan ≤ tn−1an−1 ≤ ••• ≤ tλ+1aλ+1 ≤ tλaλ ≥ tλ−1aλ−1 ≥ ••• ≥ ta1 ≥ a0, for some t > 0 and 0 < λ ≤ n.