  Let $\nu_0(t),\nu_1(t),\,\ldots\,,\nu_n(t)$ be the roots of the equation
$R(z)=t$, where $R(z)$ is a rational function of the form
\[R(z)=z+\sum\limits_{k=1}^n\frac{\alpha_k}{z-\mu_k},\] $\mu_k$ are pairwise
different real numbers, $\alpha_k>0,\,1\leq{}k\leq{}n$. Then for each real
$\xi$, the function
$e^{\xi\nu_0(t)}+e^{\xi\nu_1(t)}+\,\cdots\,+e^{\xi\nu_n(t)}$ is exponentially
convex on the interval $-\infty<t<\infty$.
