On a family of hypergeometric Sobolev orthogonal polynomials on the unit circle
| Autor: | Sergey M. Zagorodnyuk |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Matematik
Numerical Analysis Statistics::Theory Recurrence relation Sobolev orthogonal polynomials hypergeometric polynomials unit circle differential equation recurrence relation Applied Mathematics Orthogonal polynomials on the unit circle Measure (mathematics) Hypergeometric distribution 33C45 Combinatorics Sobolev space symbols.namesake Matrix (mathematics) Unit circle Mathematics - Classical Analysis and ODEs Classical Analysis and ODEs (math.CA) FOS: Mathematics symbols Jacobi polynomials Mathematics Analysis |
| Zdroj: | Volume: 3, Issue: 2 75-84 Constructive Mathematical Analysis |
| ISSN: | 2651-2939 |
| Popis: | In this paper we study the following family of hypergeometric polynomials: $y_n(x) = \frac{ (-1)^\rho }{ n! } x^n {}_2 F_0(-n,\rho;-;-\frac{1}{x})$, depending on a parameter $\rho\in\mathbb{N}$. Differential equations of orders $\rho+1$ and $2$ for these polynomials are given. A recurrence relation for $y_n$ is derived as well. Polynomials $y_n$ are Sobolev orthogonal polynomials on the unit circle with an explicit matrix measure. Comment: 11 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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