一类广义的十次Freud-型权函数

Abstract

Abstract:

In this paper, the authors focus on a generalised decic Freud-type weight function $w(x;t, \alpha)=|x|^{\alpha}{\rm e}^{-x^{10}+tx^2}, t, x\in\mathbb{R}, \alpha>-1,$ and study the properties of the orthogonal polynomials with respect to this weight. The difference-differential equations of their associated recurrence coefficients are derived; meanwhile, the authors also find the asymptotic behavior of recurrence coefficients via above mentioned equations. What's more, the authors discuss the Hankel determinant in regard to this weight as $n\rightarrow\infty$ , and calculate the smallest eigenvalues of large Hankel matrices generated by this weight when $\alpha=t=0$ .

Key words: Orthogonal Polynomials, Recurrence coefficients, Hankel determinant, Smallest eigenvalue

CLC Number:

O175.7

Dan Wang,Mengkun Zhu,Chen Yang,Xiaoli Wang. A Generalised Decic Freud-Type Weight[J].Acta mathematica scientia,Series A, 2021, 41(4): 921-935.

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References 38

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A Generalised Decic Freud-Type Weight

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