论文标题
与指数积分相关的多个正交多项式
Multiple orthogonal polynomials associated with the exponential integral
论文作者
论文摘要
我们介绍了一个新的家族，其中有两个正交多项式，以满足正交条件，相对于两个权重$（W_1，W_2）$在积极的实际线上，带有$ W_1（x）= x^αe^{ - x} $ gamma = x^αe^{ - x} $ gamma密度和$ w_2（x）= x^x^x^emention $ a d d d d d d d; $ e_ {ν+1} $。我们给出了I型功能和II型多项式的明确公式，它们的Mellin Transform，Rodrigues配方，超几何序列和复发关系。我们确定II型多个正交多项式的（缩放）零的渐近分布，并与随机矩阵理论建立联系。最后，我们还考虑了混合型多重正交多项式的相关家族。
We introduce a new family of multiple orthogonal polynomials satisfying orthogonality conditions with respect to two weights $(w_1,w_2)$ on the positive real line, with $w_1(x)=x^αe^{-x}$ the gamma density and $w_2(x) = x^αE_{ν+1}(x)$ a density related to the exponential integral $E_{ν+1}$. We give explicit formulas for the type I functions and type II polynomials, their Mellin transform, Rodrigues formulas, hypergeometric series and recurrence relations. We determine the asymptotic distribution of the (scaled) zeros of the type II multiple orthogonal polynomials and make a connection to random matrix theory. Finally, we also consider a related family of mixed type multiple orthogonal polynomials.
