Linearization and Krein-like functionals of hypergeometric orthogonal polynomials
| Autor: | I. V. Toranzo, Jesús S. Dehesa, Juan J. Moreno-Balcázar |
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| Rok vydání: | 2018 |
| Předmět: |
Weight function
Pure mathematics Logarithm 010102 general mathematics FOS: Physical sciences Statistical and Nonlinear Physics 010103 numerical & computational mathematics Interval (mathematics) Mathematical Physics (math-ph) 01 natural sciences Hypergeometric distribution Exponential function Kernel (algebra) Linearization Orthogonal polynomials 0101 mathematics Mathematical Physics Mathematics |
| DOI: | 10.48550/arxiv.1812.07231 |
| Popis: | The Krein-like $r$-functionals of the hypergeometric orthogonal polynomials $\{p_{n}(x) \}$ with kernel of the form $x^{s}[\omega(x)]^{\beta}p_{m_{1}}(x)\ldots p_{m_{r}}(x)$, being $\omega(x)$ the weight function on the interval $\Delta\in\mathbb{R}$, are determined by means of the Srivastava linearization method. The particular $2$-functionals, which are particularly relevant in quantum physics, are explicitly given in terms of the degrees and the characteristic parameters of the polynomials. They include the well-known power moments and the novel Krein-like moments. Moreover, various related types of exponential and logarithmic functionals are also investigated. Comment: Accepted in Journal of Mathematical Physics |
| Databáze: | OpenAIRE |
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