关于切比雪夫多项式的概率性质
On probabilistic aspects of Chebyshev polynomials
摘要：
}本说明的主要目标是提供新的，大多数是多维密度，compensable支持，并列出其许多属性，使有效的计算。获得这样的密度的思想是首先建立一些一维密度依赖于许多参数，然后把这样构造的分布作为条件分布。然后，当然，通过对参数施加一定的分布，并将两个分布相乘，我们得到新的多元分布。为了使有效的计算，我们利用好，简单和广泛已知的切比雪夫多项式的属性。因此，特别地，上述一维分布将具有乘以某个有理函数的反正弦分布的形式。事实上，我们使用切比雪夫多项式，使我们能够计算所有的时刻，这个一维分布，以及找到一个家庭的多项式是正交的关于这个分布。
英文摘要：
} The main goal of this note is to provide new, mostly multidimensional densities, compactly supported and list many of its properties that enable effective calculations. The idea of obtaining such densities is firstly to build some one-dimensional densities depending on many parameters and then treat the constructed in this way distributions as conditional ones. Then of course by imposing certain distribution on the parameters and multiplying the two distributions we arrive at new multivariate distribution. To enable effective calculations, we utilize nice, simple and widely known properties of Chebyshev polynomials. Thus, in particular, the one-dimensional distribution mentioned above will have a form of arcsine distribution multiplied by some rational function. The fact that we use Chebyshev polynomials allows us to calculate all moments of this one-dimensional distribution as well as to find a family of polynomials that are orthogonal with respect to this distribution.
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