Zeros of a binomial combination of Chebyshev polynomials

For $0<\alpha <1$, we study the zeros of the sequence of polynomials $\left{ P_{m}(z)\right} _{m=0}^{\infty}$generatedbythereciprocalof$(1-t)^{\alpha}(1-2zt+t^{2})$,expandedasapowerseriesin$t$. Equivalently, this sequence is obtained from a linear combination of Chebyshev polynomials whose coefficients have a binomial form. We show that the number of zeros of $P_m(z)$ outside the interval $(-1,1)$ is bounded by a constant independent of $m$.