Classical Orthogonal Polynomials of a Discrete Variable
Classical Orthogonal Polynomials of a Discrete Variable
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DOI：
10.1007/978-3-642-74748-9_2
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发表时间：
1991-10
期刊：
影响因子：
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通讯作者：
A. Nikiforov;Vasilii B. Uvarov;S. Suslov
中科院分区：
文献类型：
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作者：
A. Nikiforov;Vasilii B. Uvarov;S. Suslov
满足正交关系的多项式spn（x）的基本性质也适用于满足更一般形式的正交关系的多项式，它可以用Stielties积分表示，其中w（x）是单调非减函数（通常称为分布函数）。正交关系（2.0.2）简化为（2.0.1）在函数w（x）在（a，B）上有导数且w ′（x）= n（x）的情况下，为了解决许多问题，使用满足正交关系的正交多项式（2.0.2）在w（x）是跳跃函数的情况下，即在点x =xi处具有跳跃的分段常数函数。在这种情况下，正交关系式（2.0.2）可以改写为以下形式：
The basic properties of the polynomialspn(x) that satisfy the orthogonality relationshold also for the polynomials that satisfy the orthogonality relations of a more general form, which can be expressed in terms of Stielties integralswherew(x) is a monotonic nondecreasing function (usually called the distribution function). The orthogonality relation (2.0.2) is reduced to (2.0.1) in the case when the functionw(x) has a derivative on (a,b) andw′(x)= ϱ(x).For solving many problems orthogonal polynomials are used that satisfy the orthogonality relations (2.0.2) in the case whenw(x) is a function of jumps, i.e. the piecewise constant function with jumpsϱiat the pointsx=xi.In this case the orthogonality relation (2.0.2) can be rewritten in the form