Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (4): 921-935.

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A Generalised Decic Freud-Type Weight

Dan Wang1(),Mengkun Zhu2,*(),Chen Yang1(),Xiaoli Wang2()   

  1. 1 Department of Mathematics, Faculty of Science and Technology, University of Macau, Avenida da Universidade, Macau Taipa 999078
    2 School of Mathematics and Statistics, Qilu University of Technology(Shangdong Academy of Sciences), Jinan 250353
  • Received:2020-08-04 Online:2021-08-26 Published:2021-08-09
  • Contact: Mengkun Zhu;;;
  • Supported by:
    the Macau Science and Technology Development Fund(FDCT023/2017/A1);the Universidade de Macau(MYRG2018-00125FST);the NSFC(11801292);the NSF of Guangdong Province(2021A1515010361)


In this paper, the authors focus on a generalised decic Freud-type weight function 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