An electrostatic interpretation of the zeros of sieved ultraspherical polynomials

An electrostatic interpretation of the zeros of sieved ultraspherical polynomials

In an earlier work [Castillo et al., J. Math. Anal. Appl. 455, 1801–1821 (2017)], it was proved that the semiclassical class of orthogonal polynomials is stable under polynomial transformations. In this work, we use this fact to derive in a unified way old and new properties concerning the sieved ul...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of mathematical physics 2020-05, Vol.61 (5)
Hauptverfasser: Castillo, K., de Jesus, M. N., Petronilho, J.
Format: Artikel
Sprache:eng
Schlagworte:
Differential equations
Ordinary differential equations
Physics
Polynomials
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue 5
container_start_page
container_title Journal of mathematical physics
container_volume 61
creator Castillo, K.
de Jesus, M. N.
Petronilho, J.
description In an earlier work [Castillo et al., J. Math. Anal. Appl. 455, 1801–1821 (2017)], it was proved that the semiclassical class of orthogonal polynomials is stable under polynomial transformations. In this work, we use this fact to derive in a unified way old and new properties concerning the sieved ultraspherical polynomials of the first and second kind. In particular, we derive ordinary differential equations for these polynomials. As an application, we use the differential equation for sieved ultraspherical polynomials of the first kind to deduce that the zeros of these polynomials mark the locations of a set of particles that are in electrostatic equilibrium with respect to a particular external field.
doi_str_mv 10.1063/1.5063333
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2397913407</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2397913407</sourcerecordid><originalsourceid>FETCH-LOGICAL-c327t-5959b14a51cbf180edfa9c505f03fe87755a5f13ad6a8141b2650d789ec8a47d3</originalsourceid><addsrcrecordid>eNqdkE9LAzEQxYMoWKsHv8GCJ4Wtmc1mkz2W4j8oiKDnkGYndMt2syZpoX56U7bg3bk8HvyYmfcIuQU6A1qxR5jxJGnOyASorHNRcXlOJpQWRV6UUl6SqxA2lALIspyQj3mfYYcmeheijq3J2j6iHzweneszZ7O4xuwHE3A0ocU9Ntmui16HYY2-NbrLBtcderdtdReuyYVNgjcnnZKv56fPxWu-fH95W8yXuWGFiDmveb2CUnMwKwuSYmN1bTjlljKLUgjONbfAdFNpCSWsiorTRsgajdSlaNiU3I17B---dxii2rid79NJVbBa1MBKKhJ1P1Im_R88WjX4dqv9QQFVx8YUqFNjiX0Y2WDaMf3_4L3zf6AaGst-ATdHemI</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2397913407</pqid></control><display><type>article</type><title>An electrostatic interpretation of the zeros of sieved ultraspherical polynomials</title><source>AIP Journals Complete</source><source>Alma/SFX Local Collection</source><creator>Castillo, K. ; de Jesus, M. N. ; Petronilho, J.</creator><creatorcontrib>Castillo, K. ; de Jesus, M. N. ; Petronilho, J.</creatorcontrib><description>In an earlier work [Castillo et al., J. Math. Anal. Appl. 455, 1801–1821 (2017)], it was proved that the semiclassical class of orthogonal polynomials is stable under polynomial transformations. In this work, we use this fact to derive in a unified way old and new properties concerning the sieved ultraspherical polynomials of the first and second kind. In particular, we derive ordinary differential equations for these polynomials. As an application, we use the differential equation for sieved ultraspherical polynomials of the first kind to deduce that the zeros of these polynomials mark the locations of a set of particles that are in electrostatic equilibrium with respect to a particular external field.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/1.5063333</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><publisher>New York: American Institute of Physics</publisher><subject>Differential equations ; Ordinary differential equations ; Physics ; Polynomials</subject><ispartof>Journal of mathematical physics, 2020-05, Vol.61 (5)</ispartof><rights>Author(s)</rights><rights>2020 Author(s). Published under license by AIP Publishing.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c327t-5959b14a51cbf180edfa9c505f03fe87755a5f13ad6a8141b2650d789ec8a47d3</citedby><cites>FETCH-LOGICAL-c327t-5959b14a51cbf180edfa9c505f03fe87755a5f13ad6a8141b2650d789ec8a47d3</cites><orcidid>0000-0003-0712-7031 ; 0000-0003-4803-8182</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jmp/article-lookup/doi/10.1063/1.5063333$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>314,780,784,794,4510,27923,27924,76155</link.rule.ids></links><search><creatorcontrib>Castillo, K.</creatorcontrib><creatorcontrib>de Jesus, M. N.</creatorcontrib><creatorcontrib>Petronilho, J.</creatorcontrib><title>An electrostatic interpretation of the zeros of sieved ultraspherical polynomials</title><title>Journal of mathematical physics</title><description>In an earlier work [Castillo et al., J. Math. Anal. Appl. 455, 1801–1821 (2017)], it was proved that the semiclassical class of orthogonal polynomials is stable under polynomial transformations. In this work, we use this fact to derive in a unified way old and new properties concerning the sieved ultraspherical polynomials of the first and second kind. In particular, we derive ordinary differential equations for these polynomials. As an application, we use the differential equation for sieved ultraspherical polynomials of the first kind to deduce that the zeros of these polynomials mark the locations of a set of particles that are in electrostatic equilibrium with respect to a particular external field.</description><subject>Differential equations</subject><subject>Ordinary differential equations</subject><subject>Physics</subject><subject>Polynomials</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNqdkE9LAzEQxYMoWKsHv8GCJ4Wtmc1mkz2W4j8oiKDnkGYndMt2syZpoX56U7bg3bk8HvyYmfcIuQU6A1qxR5jxJGnOyASorHNRcXlOJpQWRV6UUl6SqxA2lALIspyQj3mfYYcmeheijq3J2j6iHzweneszZ7O4xuwHE3A0ocU9Ntmui16HYY2-NbrLBtcderdtdReuyYVNgjcnnZKv56fPxWu-fH95W8yXuWGFiDmveb2CUnMwKwuSYmN1bTjlljKLUgjONbfAdFNpCSWsiorTRsgajdSlaNiU3I17B---dxii2rid79NJVbBa1MBKKhJ1P1Im_R88WjX4dqv9QQFVx8YUqFNjiX0Y2WDaMf3_4L3zf6AaGst-ATdHemI</recordid><startdate>20200501</startdate><enddate>20200501</enddate><creator>Castillo, K.</creator><creator>de Jesus, M. N.</creator><creator>Petronilho, J.</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0003-0712-7031</orcidid><orcidid>https://orcid.org/0000-0003-4803-8182</orcidid></search><sort><creationdate>20200501</creationdate><title>An electrostatic interpretation of the zeros of sieved ultraspherical polynomials</title><author>Castillo, K. ; de Jesus, M. N. ; Petronilho, J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c327t-5959b14a51cbf180edfa9c505f03fe87755a5f13ad6a8141b2650d789ec8a47d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Differential equations</topic><topic>Ordinary differential equations</topic><topic>Physics</topic><topic>Polynomials</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Castillo, K.</creatorcontrib><creatorcontrib>de Jesus, M. N.</creatorcontrib><creatorcontrib>Petronilho, J.</creatorcontrib><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Castillo, K.</au><au>de Jesus, M. N.</au><au>Petronilho, J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An electrostatic interpretation of the zeros of sieved ultraspherical polynomials</atitle><jtitle>Journal of mathematical physics</jtitle><date>2020-05-01</date><risdate>2020</risdate><volume>61</volume><issue>5</issue><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>In an earlier work [Castillo et al., J. Math. Anal. Appl. 455, 1801–1821 (2017)], it was proved that the semiclassical class of orthogonal polynomials is stable under polynomial transformations. In this work, we use this fact to derive in a unified way old and new properties concerning the sieved ultraspherical polynomials of the first and second kind. In particular, we derive ordinary differential equations for these polynomials. As an application, we use the differential equation for sieved ultraspherical polynomials of the first kind to deduce that the zeros of these polynomials mark the locations of a set of particles that are in electrostatic equilibrium with respect to a particular external field.</abstract><cop>New York</cop><pub>American Institute of Physics</pub><doi>10.1063/1.5063333</doi><tpages>19</tpages><orcidid>https://orcid.org/0000-0003-0712-7031</orcidid><orcidid>https://orcid.org/0000-0003-4803-8182</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 0022-2488
ispartof Journal of mathematical physics, 2020-05, Vol.61 (5)
issn 0022-2488
1089-7658
language eng
recordid cdi_proquest_journals_2397913407
source AIP Journals Complete; Alma/SFX Local Collection
subjects Differential equations
Ordinary differential equations
Physics
Polynomials
title An electrostatic interpretation of the zeros of sieved ultraspherical polynomials
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-11T20%3A08%3A32IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=An%20electrostatic%20interpretation%20of%20the%20zeros%20of%20sieved%20ultraspherical%20polynomials&rft.jtitle=Journal%20of%20mathematical%20physics&rft.au=Castillo,%20K.&rft.date=2020-05-01&rft.volume=61&rft.issue=5&rft.issn=0022-2488&rft.eissn=1089-7658&rft.coden=JMAPAQ&rft_id=info:doi/10.1063/1.5063333&rft_dat=%3Cproquest_cross%3E2397913407%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2397913407&rft_id=info:pmid/&rfr_iscdi=true