On zero distribution of the sum of Gegenbauer polynomials

We study the zero distribution of the sum of the first $n$ Gegenbauer polynomials $$S_n^{(\alpha )}(z)=\sum _{k=0}^n{C}_k^{(\alpha )}(z)\mathrm{.}$$ We prove that for $\alpha >1$, the zeros of $S_n^{(\alpha )}(z)$ lie on the interval $(-1,1)$ for all large $n$.