Zeros of Taylor polynomials formed by a three-term recurrence

From a sequence \ aₙ\ ₙ₌₀∞ of real numbers satisfying a three-term recurrence, we form a sequence of polynomials \ Pₘ(z)\ ₘ₌₀∞ whose coefficients are numbers in this sequence. We showed that under explicit conditions, the zeros of Pₘ(z), m1, lie on one side of the circle whose radius is given by modulus of a zero of the denominator of the generating function of \ aₙ\ ₙ₌₀∞. 2000 Mathematics Subject Classification. 30C15, 26C10, 11C08.