The Origin and Mathematical Characteristics of the Super-Universal Associated-Legendre Polynomials

We study the mathematical characteristics of the super-universal associated-Legendre polynomials arising from a kind of double ring-shaped potentials and obtain their polar angular wave functions with certain parity. We find that there exists the even or odd parity for the polar angular wave functio...

Full description

Saved in:
Bibliographic Details
Published in:理论物理通讯：英文版 2014 (9), p.331-337
Main Author: 陈昌远 尤源 陆法林 孙东升 董世海
Format: Article
Language:English
Subjects:
associated
double
functions
hypergeometric
Jacobi
Legendre
parity
polynomials
potential
ring-shaped
super-universal
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page 337
container_issue 9
container_start_page 331
container_title 理论物理通讯：英文版
container_volume
creator 陈昌远 尤源 陆法林 孙东升 董世海
description We study the mathematical characteristics of the super-universal associated-Legendre polynomials arising from a kind of double ring-shaped potentials and obtain their polar angular wave functions with certain parity. We find that there exists the even or odd parity for the polar angular wave functions when the parameter η is taken to be positive integer, while there exist both even and odd parities when η is taken as positive non-integer real values. The relations among the super-universal associated-Legendre polynomials, the hypergeometric polynomials, and the Jacobi polynomials are also established.
format article
fullrecord <record><control><sourceid>chongqing</sourceid><recordid>TN_cdi_chongqing_primary_67738480504849524857484856</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cqvip_id>67738480504849524857484856</cqvip_id><sourcerecordid>67738480504849524857484856</sourcerecordid><originalsourceid>FETCH-chongqing_primary_677384805048495248574848563</originalsourceid><addsrcrecordid>eNqdi0sKwjAURTNQ8LuHbKCQftLGoYjiQFGwjsuzfbZP2kSTKnT3ZuAKHJ3LPfeO2FREMg7SUEQTNnPuIYSIsjScslveID9Zqklz0BU_Qt9gBz2V0PJNAxbKHi05Xzhu7txbfnk_0QZXTR-0zs_WzpmSoMcqOGCNurLIz6YdtOkIWrdg47sHLn-cs3i3zTf7oGyMrl-k6-JpqQM7FGmWxSpRQopEJSsZJUpmPimZxv-9vtlJS9E</addsrcrecordid><sourcetype>Publisher</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>The Origin and Mathematical Characteristics of the Super-Universal Associated-Legendre Polynomials</title><source>Institute of Physics:Jisc Collections:IOP Publishing Read and Publish 2024-2025 (Reading List)</source><creator>陈昌远 尤源 陆法林 孙东升 董世海</creator><creatorcontrib>陈昌远 尤源 陆法林 孙东升 董世海</creatorcontrib><description>We study the mathematical characteristics of the super-universal associated-Legendre polynomials arising from a kind of double ring-shaped potentials and obtain their polar angular wave functions with certain parity. We find that there exists the even or odd parity for the polar angular wave functions when the parameter η is taken to be positive integer, while there exist both even and odd parities when η is taken as positive non-integer real values. The relations among the super-universal associated-Legendre polynomials, the hypergeometric polynomials, and the Jacobi polynomials are also established.</description><identifier>ISSN: 0253-6102</identifier><language>eng</language><subject>associated ; double ; functions ; hypergeometric ; Jacobi ; Legendre ; parity ; polynomials ; potential ; ring-shaped ; super-universal</subject><ispartof>理论物理通讯：英文版, 2014 (9), p.331-337</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttp://image.cqvip.com/vip1000/qk/83837X/83837X.jpg</thumbnail><link.rule.ids>314,776,780,4010</link.rule.ids></links><search><creatorcontrib>陈昌远 尤源 陆法林 孙东升 董世海</creatorcontrib><title>The Origin and Mathematical Characteristics of the Super-Universal Associated-Legendre Polynomials</title><title>理论物理通讯：英文版</title><addtitle>Communications in Theoretical Physics</addtitle><description>We study the mathematical characteristics of the super-universal associated-Legendre polynomials arising from a kind of double ring-shaped potentials and obtain their polar angular wave functions with certain parity. We find that there exists the even or odd parity for the polar angular wave functions when the parameter η is taken to be positive integer, while there exist both even and odd parities when η is taken as positive non-integer real values. The relations among the super-universal associated-Legendre polynomials, the hypergeometric polynomials, and the Jacobi polynomials are also established.</description><subject>associated</subject><subject>double</subject><subject>functions</subject><subject>hypergeometric</subject><subject>Jacobi</subject><subject>Legendre</subject><subject>parity</subject><subject>polynomials</subject><subject>potential</subject><subject>ring-shaped</subject><subject>super-universal</subject><issn>0253-6102</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNqdi0sKwjAURTNQ8LuHbKCQftLGoYjiQFGwjsuzfbZP2kSTKnT3ZuAKHJ3LPfeO2FREMg7SUEQTNnPuIYSIsjScslveID9Zqklz0BU_Qt9gBz2V0PJNAxbKHi05Xzhu7txbfnk_0QZXTR-0zs_WzpmSoMcqOGCNurLIz6YdtOkIWrdg47sHLn-cs3i3zTf7oGyMrl-k6-JpqQM7FGmWxSpRQopEJSsZJUpmPimZxv-9vtlJS9E</recordid><startdate>2014</startdate><enddate>2014</enddate><creator>陈昌远 尤源 陆法林 孙东升 董世海</creator><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope></search><sort><creationdate>2014</creationdate><title>The Origin and Mathematical Characteristics of the Super-Universal Associated-Legendre Polynomials</title><author>陈昌远 尤源 陆法林 孙东升 董世海</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-chongqing_primary_677384805048495248574848563</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>associated</topic><topic>double</topic><topic>functions</topic><topic>hypergeometric</topic><topic>Jacobi</topic><topic>Legendre</topic><topic>parity</topic><topic>polynomials</topic><topic>potential</topic><topic>ring-shaped</topic><topic>super-universal</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>陈昌远 尤源 陆法林 孙东升 董世海</creatorcontrib><collection>维普_期刊</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>中文科技期刊数据库-7.0平台</collection><collection>中文科技期刊数据库- 镜像站点</collection><jtitle>理论物理通讯：英文版</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>陈昌远 尤源 陆法林 孙东升 董世海</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Origin and Mathematical Characteristics of the Super-Universal Associated-Legendre Polynomials</atitle><jtitle>理论物理通讯：英文版</jtitle><addtitle>Communications in Theoretical Physics</addtitle><date>2014</date><risdate>2014</risdate><issue>9</issue><spage>331</spage><epage>337</epage><pages>331-337</pages><issn>0253-6102</issn><abstract>We study the mathematical characteristics of the super-universal associated-Legendre polynomials arising from a kind of double ring-shaped potentials and obtain their polar angular wave functions with certain parity. We find that there exists the even or odd parity for the polar angular wave functions when the parameter η is taken to be positive integer, while there exist both even and odd parities when η is taken as positive non-integer real values. The relations among the super-universal associated-Legendre polynomials, the hypergeometric polynomials, and the Jacobi polynomials are also established.</abstract></addata></record>
fulltext fulltext
identifier ISSN: 0253-6102
ispartof 理论物理通讯：英文版, 2014 (9), p.331-337
issn 0253-6102
language eng
recordid cdi_chongqing_primary_67738480504849524857484856
source Institute of Physics:Jisc Collections:IOP Publishing Read and Publish 2024-2025 (Reading List)
subjects associated
double
functions
hypergeometric
Jacobi
Legendre
parity
polynomials
potential
ring-shaped
super-universal
title The Origin and Mathematical Characteristics of the Super-Universal Associated-Legendre Polynomials
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-04T12%3A35%3A59IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-chongqing&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20Origin%20and%20Mathematical%20Characteristics%20of%20the%20Super-Universal%20Associated-Legendre%20Polynomials&rft.jtitle=%E7%90%86%E8%AE%BA%E7%89%A9%E7%90%86%E9%80%9A%E8%AE%AF%EF%BC%9A%E8%8B%B1%E6%96%87%E7%89%88&rft.au=%E9%99%88%E6%98%8C%E8%BF%9C%20%E5%B0%A4%E6%BA%90%20%E9%99%86%E6%B3%95%E6%9E%97%20%E5%AD%99%E4%B8%9C%E5%8D%87%20%E8%91%A3%E4%B8%96%E6%B5%B7&rft.date=2014&rft.issue=9&rft.spage=331&rft.epage=337&rft.pages=331-337&rft.issn=0253-6102&rft_id=info:doi/&rft_dat=%3Cchongqing%3E67738480504849524857484856%3C/chongqing%3E%3Cgrp_id%3Ecdi_FETCH-chongqing_primary_677384805048495248574848563%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_cqvip_id=67738480504849524857484856&rfr_iscdi=true