The Classical Orthogonal Polynomials
The Classical Orthogonal Polynomials
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经典正交多项式
DOI：
10.1142/9700
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
B. Doman
中科院分区：
文献类型：
--
作者：
B. Doman
这本书定义了正交多项式的集合，并推导出任何这样的集合所满足的一些性质。第一章定义了两个函数的正交性条件。然后，它给出了一个迭代过程，以产生一组相互正交的多项式，然后描述了任何一组正交多项式所满足的一些性质。当权函数在正交条件下具有特定的形式时，就产生了经典的正交多项式。这些多项式有进一步的一组属性，特别是满足一个二阶微分方程。每一个后续章节调查的性质，一个特定的多项式集从其微分方程。
This book defines sets of orthogonal polynomials and derives a number of properties satisfied by any such set. It continues by describing the classical orthogonal polynomials and the additional properties they have.The first chapter defines the orthogonality condition for two functions. It then gives an iterative process to produce a set of polynomials which are orthogonal to one another and then describes a number of properties satisfied by any set of orthogonal polynomials. The classical orthogonal polynomials arise when the weight function in the orthogonality condition has a particular form. These polynomials have a further set of properties and in particular satisfy a second order differential equation.Each subsequent chapter investigates the properties of a particular polynomial set starting from its differential equation.