Zeros of Taylor polynomials formed by a three-term recurrence

Abstract: From a sequence $\left{ a_{n}\right} {n=0}^{\infty}$ of real numbers satisfying a three-term recurrence, we form a sequence of polynomials $\left{ P{m}(z)\right} {m=0}^{\infty}$ whose coefficients are numbers in this sequence. We showed that under explicit conditions, the zeros of $P{m}(z)$, $m\gg1$, lie on one side of the circle whose radius is given by modulus of a zero of the denominator of the generating function of $\left{ a_{n}\right} _{n=0}^{\infty}$.