论文标题
一种正交性的组成方法和非古典权重的正交多项式的新序列
A method of composition orthogonality and new sequences of orthogonal polynomials and functions for non-classical weights
论文作者
论文摘要
引入了一种新的组成正交方法。它用于生成正交多项式和函数的新序列。特别是，经典的正交多项式是通过组成正交性的意义来解释的。 Finally, new sequences of orthogonal polynomials with respect to the weight function $x^αρ^2_ν(x), ρ_ν(x)= 2 x^{ν/2} K_ν(2\sqrt x),\ x >0, ν\ge 0, α> -1$, where $K_ν(z)$ is the modified Bessel function or Macdonald function, are investigated.获得了差异特性，复发关系，显式表示，生成函数和Rodrigues-type公式。表现出相应的多个正交多项式。
A new method of composition orthogonality is introduced. It is applied to generate new sequences of orthogonal polynomials and functions. In particular, classical orthogonal polynomials are interpreted in the sense of composition orthogonality. Finally, new sequences of orthogonal polynomials with respect to the weight function $x^αρ^2_ν(x), ρ_ν(x)= 2 x^{ν/2} K_ν(2\sqrt x),\ x >0, ν\ge 0, α> -1$, where $K_ν(z)$ is the modified Bessel function or Macdonald function, are investigated. Differential properties, recurrence relations, explicit representations, generating functions and Rodrigues-type formulae are obtained. The corresponding multiple orthogonal polynomials are exhibited.
