A generalization of classical orthogonal polynomials and the convergence of simultaneous Pade approximants
A generalization of classical orthogonal polynomials and the convergence of simultaneous Pade approximants
复制标题
经典正交多项式的推广和联立Pade逼近的收敛
DOI：
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
V. Sorokin
中科院分区：
文献类型：
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作者：
V. Sorokin
引入了广义经典多正交多项式的概念，特别是广义Laguerre多项式，它对应于复平面上无限射线上的测度集合.研究了这些多项式及其相应的第二类函数的渐近行为。此外，广义的贝塞尔函数和第二类欧拉积分的定义和调查。证明了某些Stieltjes型函数的联立Pade逼近的收敛性。
The concept of generalized classical polyorthogonal polynomials and, in particular, that of generalized Laguerre polynomials, corresponding to a collection of measures with supports on infinite rays in the complex plane, is introduced. The asymptotic behavior of these polynomials and of their corresponding functions of the second kind is investigated. Moreover, generalizations of the Bessel functions and of the Euler integral of the second kind are defined and investigated. The convergence of the simultaneous Pade approximants to certain Stieltjes type functions is proved.