|
Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Structure Relations of Classical Orthogonal Polynomials in the Quadratic and $q$-Quadratic Variable
Maurice Kenfack Nanghoab, Kerstin Jordaanc a Department of Mathematics and Computer Science, University of Dschang, Cameroon
b Department of Mathematics and Applied Mathematics, University of Pretoria,
Private bag X20 Hatfield, 0028 Pretoria, South Africa
c Department of Decision Sciences, University of South Africa, PO Box 392, Pretoria, 0003, South Africa
Аннотация:
We prove an equivalence between the existence of the first structure relation satisfied by a sequence of monic orthogonal polynomials $\{P_n\}_{n=0}^{\infty}$, the orthogonality of the second derivatives $\{\mathbb{D}_{x}^2P_n\}_{n= 2}^{\infty}$ and a generalized Sturm–Liouville type equation. Our treatment of the generalized Bochner theorem leads to explicit solutions of the difference equation [Vinet L., Zhedanov A., J. Comput. Appl. Math. 211 (2008), 45–56], which proves that the only monic orthogonal polynomials that satisfy the first structure relation are Wilson polynomials, continuous dual Hahn polynomials, Askey–Wilson polynomials and their special or limiting cases as one or more parameters tend to $\infty$. This work extends our previous result [arXiv:1711.03349] concerning a conjecture due to Ismail. We also derive a second structure relation for polynomials satisfying the first structure relation.
Ключевые слова:
classical orthogonal polynomials; classical $q$-orthogonal polynomials; Askey–Wilson polynomials; Wilson polynomials; structure relations; characterization theorems.
Поступила: 31 января 2018 г.; в окончательном варианте 13 ноября 2018 г.; опубликована 27 ноября 2018 г.
Образец цитирования:
Maurice Kenfack Nangho, Kerstin Jordaan, “Structure Relations of Classical Orthogonal Polynomials in the Quadratic and $q$-Quadratic Variable”, SIGMA, 14 (2018), 126, 26 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1425 https://www.mathnet.ru/rus/sigma/v14/p126
|
Статистика просмотров: |
Страница аннотации: | 126 | PDF полного текста: | 29 | Список литературы: | 20 |
|