Generating Some Symmetric Semi-classical Orthogonal Polynomials

Canadian mathematical bulletin

Mohamed Zaatra¹ 

[1] Institut Supérieur des Sciences et Techniques des Eaux de Gabès, Campus universitaire, Gabès 6072, Tunisia

关键词: orthogonal polynomials;    quadratic decomposition;    semi-classical forms;    structure relation;   

DOI  :  10.4153/CMB-2015-041-9

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We show that if $v$ is a regular semi-classical form(linear functional), then the symmetric form $u$ defined by therelation $x^{2}sigma u = -lambda v$,where $(sigma f)(x)=f(x^{2})$ and the oddmoments of $u$ are $0$, is also regular and semi-classical form for everycomplex $lambda $ except for a discrete set of numbers dependingon $v$. We give explicitly the three-term recurrence relationand thestructure relation coefficients of the orthogonal polynomialssequence associated with $u$ and the class of the form $u$ knowingthat of $v$. We conclude with an illustrative example.

【 授权许可】

Unknown