Let \(H(D)\) denote the set of analytic functions in \(D= \{z\in\mathbb{C}:|z|< 1\}\) and \(H_0(D)\) the subset of \(H(D)\) whose members are normalized \(f(0)= 0\), \(f'(0)= 1\). For \(F(z)= \sum_{k=0} a_k z^k\), \(G(z)= \sum_{k=0} b_k z^k\) belonging to \(H(D)\) we define the Hadamard product as \((F* G)(z)= \sum^\infty_{k=0} a_k b_k z^k\). We say that \(f\in H_0(D)\) is prestarlike of order \(\alpha\) if \(f*{z\over (1-z)^{2(1-\alpha)}}\) is an \(\alpha\)-starlike function. We write then \(f\in R_\alpha\). S. P. Robinson in his thesis ``Approximate Identities for Certain Dual Classes'', University of York, 1996, introduced the polynomials \[ p^\beta_n(z)= 1+ \sum^n_{k=1} \prod^{k-1}_{j=0} {n-j\over \beta+ n+ j} z^k,\quad n\in\mathbb{N},\quad \beta\geq 1 \] and made the conjecture that \(zp^\beta_n(z)\in R_{{3-\beta\over 2}}\). In this paper the authors proved this conjecture for some generalized functions which are the special hypergeometric functions \[ p^\beta_\lambda(z):= {_2F_1}(1, -\lambda,\lambda+ \beta,-1),\quad \lambda\geq-1,\quad \beta\geq 1. \] Theorem. For \(\beta\geq \max\{1,-2\lambda\}\) we have \(zp^\beta_\lambda(z)\in R_{{3-\beta\over 2}}\), and for \(0\leq \lambda_1\leq \lambda_2\), \(1\leq \beta_2\leq \beta_1\) we have \(p^{\beta_1}_{\lambda_1}\prec p^{\beta_2}_{\lambda_2}\), where ``\(\prec\)'' stands for the subordination. We can easily verify that \(p^\beta_\lambda(z)\) agrees with Robinson's definition for \(\lambda= n\in\mathbb{N}\).