论文标题
在新的两种正交多项式中，II_的积分表示
On a new class of 2-orthogonal polynomials, II_The integral representations
论文作者
论文摘要
在Douak K＆Maroni P中介绍了一对相对于一对线性功能$（U_0，U_1）$满足正交条件的新的两种正交多项式，在Douak K＆Maroni P中介绍了一对正交条件。积分变换规格功能。 2021; 32（2）：134-153]。那里指出了六个有趣的特殊案例。对于每种情况，我们精确地处理了与这些多项式相关的功能的积分表示问题。重点是矩阵微分方程$ \ big（{\bfφu} \ big）'+{\ bfinu} = 0 $，带有$ {\ bf u} = {^t}（^t}（^t}（u_0，u_1，u_1），u_1）$ and $ {\bfφ} $，$ {\ bf bf bf bf bf bf art $ {建立两个功能满足的微分方程。基于此，根据情况，我们表明$ u_0 $和$ u_1 $是通过实际行或正面线上支持的权重功能表示的，并根据各种特殊功能定义。为了使某些积分表示存在，需要添加Dirac质量。
A new class of 2-orthogonal polynomials satisfying orthogonality conditions with respect to a pair of linear functionals $(u_0,u_1)$ was presented in Douak K & Maroni P [On a new class of 2-orthogonal polynomials, I: the recurrence relations and some properties. Integral Transforms Spec Funct. 2021;32(2):134-153]. Six interesting special cases were pointed out there. For each case, we precisely deal with the integral representation problem for the functionals associated to these polynomials. The focus is on the matrix differential equation $\big({\bfΦU}\big)'+{\bfΨU}=0$, with ${\bf U}={^t}(u_0 , u_1)$ and ${\bfΦ}$, ${\bfΨ}$ are $2\times2$ polynomial matrices, from which we establish the differential equations satisfied by the two functionals. Based on this, depending on the case, we show that $u_0$ and $u_1$ are represented via weight functions supported on the real line or positive real line and defined in terms of various special functions. In order for certain integral representations to exist, addition of Dirac mass is necessary.
