论文标题
关于高阶的Kravchuk-Sobolev型多项式的差异方程式
On difference equations of Kravchuk-Sobolev type polynomials of higher order
论文作者
论文摘要
在这项贡献中，我们考虑了相对于Sobolev-Type内部产品\ [\ LEFT \ langle f，g \ rangle _ {λ，μ} \！= \！\！\！ p^x（1-p）^{n-x}} {γ（n-x+1）γ（x+1）}+λδ^j f（0）δ^j g（0）+μΔ n \ in \ mathbb z _ {+} $，$ j \ in \ mathbb z _ {+} $和$δ$表示前向差异运算符。我们得出这些多项式的明确表示。此外，还获得了与这些多项式相关的梯子算子。结果，还给出了二阶的线性差方程。
In this contribution we consider sequences of monic polynomials orthogonal with respect to Sobolev-type inner product \[ \left\langle f,g\right\rangle _{λ,μ}\!=\!\sum_{x=0}^Nf(x)g(x)\frac{Γ(N+1) p^x(1-p)^{N-x} }{Γ(N-x+1) Γ(x+1) }+λΔ^j f(0)Δ^j g(0)+μΔ^j f(N)Δ^j g(N), \] where $0<p <1$, $λ,μ\in \mathbb R_{+}$, $n\leq N\in \mathbb Z_{+}$, $j\in \mathbb Z_{+}$ and $Δ$ denotes the forward difference operators. We derive an explicit representation for these polynomials. In addition, the ladder operators associated with these polynomials are obtained. As a consequence, the linear difference equations of second order are also given.
