Meixner type polynomials ${\left(q_n\right)}_{n\ge 0}$ are defined from the Meixner polynomials by using Casoratian determinants whose entries belong to two given finite sets of polynomials ${\left({\mathcal{S}}_h\right)}_{h=1}^{m_1}$ and ${\left({\mathcal{T}}_g\right)}_{g=1}^{m_2}$. They are eigenfunctions of higher order difference operators but only for a careful choice of the polynomials ${\left({\mathcal{S}}_h\right)}_{h=1}^{m_1}$ and ${\left({\mathcal{T}}_g\right)}_{g=1}^{m_2}$, the sequence ${\left(q_n\right)}_{n\ge 0}$ is orthogonal with respect to a measure. In this paper, we prove that the Meixner type polynomials ${\left(q_n\right)}_{n\ge 0}$ always satisfy higher order recurrence relations (hence, they are bispectral). We also introduce and characterize the algebra of difference operators associated to these recurrence relations. Our characterization is constructive and surprisingly simple. As a consequence, we determine the unique choice of the polynomials ${\left({\mathcal{S}}_h\right)}_{h=1}^{m_1}$ and ${\left({\mathcal{T}}_g\right)}_{g=1}^{m_2}$ such that the sequence ${\left(q_n\right)}_{n\ge 0}$ is orthogonal with respect to a measure.

Meixner型多项式 ${（q_{ñ}）}_{ñ\ge 0}$ 是由Meixner多项式通过使用Casoratian行列式定义的，这些项的条目属于两个给定的有限多项式集 ${（{\mathcal{小号}}_H）}_{H=\mathrm{1个}}^{{米}_{\mathrm{1个}}}$ 和 ${（{\mathcal{Ť}}_G）}_{G=\mathrm{1个}}^{{米}_2}$。它们是高阶差分算子的本征函数，但仅用于仔细选择多项式${（{\mathcal{小号}}_H）}_{H=\mathrm{1个}}^{{米}_{\mathrm{1个}}}$ 和 ${（{\mathcal{Ť}}_G）}_{G=\mathrm{1个}}^{{米}_2}$， 序列 ${（q_{ñ}）}_{ñ\ge 0}$相对于度量正交。在本文中，我们证明了Meixner型多项式${（q_{ñ}）}_{ñ\ge 0}$总是满足更高阶的递归关系（因此，它们是双谱的）。我们还将介绍和表征与这些递归关系相关的差分算子的代数。我们的特征是建设性的，而且出奇的简单。结果，我们确定多项式的唯一选择${（{\mathcal{小号}}_H）}_{H=\mathrm{1个}}^{{米}_{\mathrm{1个}}}$ 和 ${（{\mathcal{Ť}}_G）}_{G=\mathrm{1个}}^{{米}_2}$ 这样的顺序 ${（q_{ñ}）}_{ñ\ge 0}$ 相对于度量正交。