A Unified Approach to Computing the Zeros of Orthogonal Polynomials
We present a unified approach to calculating the zeros of the classical orthogonal polynomials and discuss the electrostatic interpretation and its connection to the energy minimization problem. This approach works for the generalized Bessel polynomials, including the normalized reversed variant, as...
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| Format: | Article |
| Language: | English |
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Naim Çağman
2023-12-01
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| Series: | Journal of New Theory |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3364839 |
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| _version_ | 1850079840360726528 |
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| author | Ridha Moussa James Tipton |
| author_facet | Ridha Moussa James Tipton |
| author_sort | Ridha Moussa |
| collection | DOAJ |
| description | We present a unified approach to calculating the zeros of the classical orthogonal polynomials and discuss the electrostatic interpretation and its connection to the energy minimization problem. This approach works for the generalized Bessel polynomials, including the normalized reversed variant, as well as the Viet\'e--Pell and Viet\'e--Pell--Lucas polynomials. We briefly discuss the electrostatic interpretation for each aforesaid case and some recent advances. We provide zeros and error estimates for various cases of the Jacobi, Hermite, and Laguerre polynomials and offer a brief discussion of how the method was implemented symbolically and numerically with Maple. In conclusion, we provide possible avenues for future research. |
| format | Article |
| id | doaj-art-a861e9ced9184e578ceef17a4dfced6e |
| institution | DOAJ |
| issn | 2149-1402 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Naim Çağman |
| record_format | Article |
| series | Journal of New Theory |
| spelling | doaj-art-a861e9ced9184e578ceef17a4dfced6e2025-08-20T02:45:06ZengNaim ÇağmanJournal of New Theory2149-14022023-12-0145304510.53570/jnt.13505022425A Unified Approach to Computing the Zeros of Orthogonal PolynomialsRidha Moussa0https://orcid.org/0009-0009-4936-8555James Tipton1https://orcid.org/0000-0002-4291-5984Norfolk State UniversityNorfolk State UniversityWe present a unified approach to calculating the zeros of the classical orthogonal polynomials and discuss the electrostatic interpretation and its connection to the energy minimization problem. This approach works for the generalized Bessel polynomials, including the normalized reversed variant, as well as the Viet\'e--Pell and Viet\'e--Pell--Lucas polynomials. We briefly discuss the electrostatic interpretation for each aforesaid case and some recent advances. We provide zeros and error estimates for various cases of the Jacobi, Hermite, and Laguerre polynomials and offer a brief discussion of how the method was implemented symbolically and numerically with Maple. In conclusion, we provide possible avenues for future research.https://dergipark.org.tr/en/download/article-file/3364839orthogonal polynomialszeroselectrostatic interpretation |
| spellingShingle | Ridha Moussa James Tipton A Unified Approach to Computing the Zeros of Orthogonal Polynomials Journal of New Theory orthogonal polynomials zeros electrostatic interpretation |
| title | A Unified Approach to Computing the Zeros of Orthogonal Polynomials |
| title_full | A Unified Approach to Computing the Zeros of Orthogonal Polynomials |
| title_fullStr | A Unified Approach to Computing the Zeros of Orthogonal Polynomials |
| title_full_unstemmed | A Unified Approach to Computing the Zeros of Orthogonal Polynomials |
| title_short | A Unified Approach to Computing the Zeros of Orthogonal Polynomials |
| title_sort | unified approach to computing the zeros of orthogonal polynomials |
| topic | orthogonal polynomials zeros electrostatic interpretation |
| url | https://dergipark.org.tr/en/download/article-file/3364839 |
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