2 \cos \kappa_{j,n}}, \quad j=1,\ldots, n, \quad n\in \Lambda.$$ Taking into account that $\displaystyle \varphi(\zeta)=\zeta+\sqrt{\zeta^2+1}$ we see that the above expression is reduced to (\[aonesol\]) when $\zeta$ goes to infinity.

Connection with orthogonal polynomials {#sec:2}
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Let $\mu$ be a positive finite Borel measure with infinitely many points in its support $\mbox{supp}(\mu)$. Set $\Delta$ denoting the least interval which contains $\mbox{supp}(\mu)$. A collection of monic polynomials $\displaystyle \left\{q_{\mu,n}\right\}_{n \in \mathbb{Z}_+},$ $\mathbb{Z}_+=\left\{0,1,\ldots\right\}$ is the family orthogonal polynomials with respect to $\mu$ if its elements satisfy the following orthogonality relations $$\label{ortoargentino}
0=\int  x^{\nu} q_{\mu,n}(x) \, \mbox{d} \mu(x), \quad \nu=0,1,\ldots, n-1, \quad n\in \mathbb{Z}_+.$$ Each $q_{\mu,n}$ has $n$ single roots lying in the interior of $\Delta$ (we denote $\displaystyle \overset{\circ}{\Delta}$) such that it vanishes at most once in each interval of $\displaystyle \Delta \setminus \mbox{supp}(\mu)$ (see [@chi Theorem 5.2] or [@freud Chapter 1]). We also know that $q_{\mu,n+1}$ and $q_{\mu,n}$ interlace their zeros. In [@We] B. Wendroff proved that given two polynomials $P_n$ and $P_{n+1}$, with $\deg P_{n+1}=\deg P_n+1=n+1$, that interlace zeros, there always exist measures $\mu$ such that $P_n=q_{\mu,n}$ and $P_{n+1}=q_{\mu,n+1}$. Now we find some of these measures.

We say then a polynomial $\displaystyle P_n(x)=\prod_{j=1}^n\left(x-x_{j}\right)$ of degree $n$ is admissible with respect 