论文标题
由广义sturm-liouville定理产生的有限类型的不完整的对称正交多项式
Incomplete Symmetric Orthogonal Polynomials of Finite Type Generated by a Generalized Sturm-Liouville Theorem
论文作者
论文摘要
在经典的情况下，正交多项式序列的方式使$ n $ th polyenmial具有确切的度量$ n $。此类序列是完整的，并构成了任何任意多项式的空间的基础。在本文中，我们介绍了一些不包含所有学位的有限正交多项式集合，但它们是一些对称性广义sturm-liouville问题的解决方案。尽管此类多项式没有像经典情况下那样具有所有属性，但它们可以应用于函数近似理论，因为我们将计算其显式的Norm Square值。
In a classical case, orthogonal polynomial sequences are in such a way that the $ n $th polynomial has the exact degree $n$. Such sequences are complete and form a basis of the space for any arbitrary polynomial. In this paper, we introduce some incomplete sets of finite orthogonal polynomials that do not contain all degrees but they are solutions of some symmetric generalized Sturm-Liouville problems. Although such polynomials do not possess all properties as in classical cases, they can be applied to functions approximation theory as we will compute their explicit norm square values.
