On zero behavior of higher-order Sobolev-type discrete q-Hermite I orthogonal polynomials
In this work, we investigate the sequence of monic q-Hermite I-Sobolev type orthogonal polynomials of higher-order, denoted by {Hn(x;q)}n≥0, which are orthogonal with respect to the following non-standard inner product involving q-differences: ⟨p,q⟩λ=∫−11f(x)g(x)(qx,−qx;q)∞dq(x)+λ(Dqjf)(α)(Dqjg)(α),...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad de Alcalá (UAH) |
| Repositorio: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Idioma: | inglés |
| OAI Identifier: | oai:ebuah.uah.es:10017/62240 |
| Acceso en línea: | http://hdl.handle.net/10017/62240 https://dx.doi.org/10.1007/s11075-024-01868-y |
| Access Level: | acceso abierto |
| Palabra clave: | Orthogonal polynomials Sobolev-type orthogonal polynomials q-Hermite polynomials q-Hypergeometric series Matemáticas Mathematics |
| Sumario: | In this work, we investigate the sequence of monic q-Hermite I-Sobolev type orthogonal polynomials of higher-order, denoted by {Hn(x;q)}n≥0, which are orthogonal with respect to the following non-standard inner product involving q-differences: ⟨p,q⟩λ=∫−11f(x)g(x)(qx,−qx;q)∞dq(x)+λ(Dqjf)(α)(Dqjg)(α), where λ belongs to the set of positive real numbers, Dqj denotes the j-th q -discrete analogue of the derivative operator, qjα∈R∖(−1,1), and (qx,−qx;q)∞dq(x) denotes the orthogonality weight with its points of increase in a geometric progression. Connection formulas between these polynomials and standard q-Hermite I polynomials are deduced. The basic hypergeometric representation of Hn(x;q) is obtained. Moreover, for certain real values of α satisfying the condition qjα∈R∖(−1,1), we present results concerning the location of the zeros of Hn(x;q) and perform a comprehensive analysis of their asymptotic behavior as the parameter λ tends to infinity. |
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