Solutions of the Helmholtz equation for a class of non-separable cylindrical and rotational coordinate systems

In cylindrical and rotational coordinate systems, one of the variables can be separated out of the Helmholtz equation, leaving a second order partial differential equation in two variables. For a class of the coordinate systems, this equation is reducible to a recurrence set of ordinary differential...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Quarterly of applied mathematics 1958-01, Vol.15 (4), p.420-427
1. Verfasser:	Weston, Vaughan H.
Format:	Artikel
Sprache:	eng
Schlagworte:	Coefficients Cylindrical coordinates Integers Marital property Ordinary differential equations Power series Recurrence relations Research article
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page	427
container_issue	4
container_start_page	420
container_title	Quarterly of applied mathematics
container_volume	15
creator	Weston, Vaughan H.
description	In cylindrical and rotational coordinate systems, one of the variables can be separated out of the Helmholtz equation, leaving a second order partial differential equation in two variables. For a class of the coordinate systems, this equation is reducible to a recurrence set of ordinary differential equations in one variable, which are solvable by ordinary methods.
doi_str_mv	10.1090/qam/98238
format	Article
fullrecord	<record><control><sourceid>jstor_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1090_qam_98238</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>43634504</jstor_id><sourcerecordid>43634504</sourcerecordid><originalsourceid>FETCH-LOGICAL-a1608-69a3400795e512f341afe00fec9f593eb05a8b73736fa0f831ba55dff5c8a8bd3</originalsourceid><addsrcrecordid>eNp9kD1PwzAURS0EEuVj4AcgeWBhCH2u7dQeUQUUqRIDILFFL46tpnLi1naH8utJW8TI9HR1zrvDJeSGwQMDDeMNdmOtJlydkBGTclIIoeQpGQFwXshSf52Ti5RWQxwojEj_Hvw2t6FPNDial5bOre-Wwedvajdb3CPqQqRIjcd0sPrQF8muMWLtLTU73_ZNbA16in1DY8iHryGaEGLT9pgtTbuUbZeuyJlDn-z1770kn89PH7N5sXh7eZ09LgpkJaii1MgFwFRLK9nEccHQWQBnjXZSc1uDRFVP-ZSXDsEpzmqUsnFOGjWAhl-S-2OviSGlaF21jm2HcVcxqPZDVcNQ1WGowb09uquUQ_wTBS-5kCAGfnfk2KV_an4AKbtzfQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Solutions of the Helmholtz equation for a class of non-separable cylindrical and rotational coordinate systems</title><source>JSTOR Mathematics and Statistics</source><source>American Mathematical Society Journals and Series</source><source>JSTOR Complete Journals</source><source>American Mathematical Society Publications (Freely Accessible)</source><source>EZB Electronic Journals Library</source><creator>Weston, Vaughan H.</creator><creatorcontrib>Weston, Vaughan H.</creatorcontrib><description>In cylindrical and rotational coordinate systems, one of the variables can be separated out of the Helmholtz equation, leaving a second order partial differential equation in two variables. For a class of the coordinate systems, this equation is reducible to a recurrence set of ordinary differential equations in one variable, which are solvable by ordinary methods.</description><identifier>ISSN: 0033-569X</identifier><identifier>EISSN: 1552-4485</identifier><identifier>DOI: 10.1090/qam/98238</identifier><language>eng</language><publisher>Providence, Rhode Island: American Mathematical Society</publisher><subject>Coefficients ; Cylindrical coordinates ; Integers ; Marital property ; Ordinary differential equations ; Power series ; Recurrence relations ; Research article</subject><ispartof>Quarterly of applied mathematics, 1958-01, Vol.15 (4), p.420-427</ispartof><rights>Copyright 1958 American Mathematical Society</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a1608-69a3400795e512f341afe00fec9f593eb05a8b73736fa0f831ba55dff5c8a8bd3</citedby><cites>FETCH-LOGICAL-a1608-69a3400795e512f341afe00fec9f593eb05a8b73736fa0f831ba55dff5c8a8bd3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/43634504$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/43634504$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,776,780,799,828,27901,27902,57992,57996,58225,58229</link.rule.ids></links><search><creatorcontrib>Weston, Vaughan H.</creatorcontrib><title>Solutions of the Helmholtz equation for a class of non-separable cylindrical and rotational coordinate systems</title><title>Quarterly of applied mathematics</title><addtitle>Quart. Appl. Math</addtitle><description>In cylindrical and rotational coordinate systems, one of the variables can be separated out of the Helmholtz equation, leaving a second order partial differential equation in two variables. For a class of the coordinate systems, this equation is reducible to a recurrence set of ordinary differential equations in one variable, which are solvable by ordinary methods.</description><subject>Coefficients</subject><subject>Cylindrical coordinates</subject><subject>Integers</subject><subject>Marital property</subject><subject>Ordinary differential equations</subject><subject>Power series</subject><subject>Recurrence relations</subject><subject>Research article</subject><issn>0033-569X</issn><issn>1552-4485</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1958</creationdate><recordtype>article</recordtype><recordid>eNp9kD1PwzAURS0EEuVj4AcgeWBhCH2u7dQeUQUUqRIDILFFL46tpnLi1naH8utJW8TI9HR1zrvDJeSGwQMDDeMNdmOtJlydkBGTclIIoeQpGQFwXshSf52Ti5RWQxwojEj_Hvw2t6FPNDial5bOre-Wwedvajdb3CPqQqRIjcd0sPrQF8muMWLtLTU73_ZNbA16in1DY8iHryGaEGLT9pgtTbuUbZeuyJlDn-z1770kn89PH7N5sXh7eZ09LgpkJaii1MgFwFRLK9nEccHQWQBnjXZSc1uDRFVP-ZSXDsEpzmqUsnFOGjWAhl-S-2OviSGlaF21jm2HcVcxqPZDVcNQ1WGowb09uquUQ_wTBS-5kCAGfnfk2KV_an4AKbtzfQ</recordid><startdate>19580101</startdate><enddate>19580101</enddate><creator>Weston, Vaughan H.</creator><general>American Mathematical Society</general><general>Brown University</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19580101</creationdate><title>Solutions of the Helmholtz equation for a class of non-separable cylindrical and rotational coordinate systems</title><author>Weston, Vaughan H.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a1608-69a3400795e512f341afe00fec9f593eb05a8b73736fa0f831ba55dff5c8a8bd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1958</creationdate><topic>Coefficients</topic><topic>Cylindrical coordinates</topic><topic>Integers</topic><topic>Marital property</topic><topic>Ordinary differential equations</topic><topic>Power series</topic><topic>Recurrence relations</topic><topic>Research article</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Weston, Vaughan H.</creatorcontrib><collection>CrossRef</collection><jtitle>Quarterly of applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Weston, Vaughan H.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Solutions of the Helmholtz equation for a class of non-separable cylindrical and rotational coordinate systems</atitle><jtitle>Quarterly of applied mathematics</jtitle><stitle>Quart. Appl. Math</stitle><date>1958-01-01</date><risdate>1958</risdate><volume>15</volume><issue>4</issue><spage>420</spage><epage>427</epage><pages>420-427</pages><issn>0033-569X</issn><eissn>1552-4485</eissn><abstract>In cylindrical and rotational coordinate systems, one of the variables can be separated out of the Helmholtz equation, leaving a second order partial differential equation in two variables. For a class of the coordinate systems, this equation is reducible to a recurrence set of ordinary differential equations in one variable, which are solvable by ordinary methods.</abstract><cop>Providence, Rhode Island</cop><pub>American Mathematical Society</pub><doi>10.1090/qam/98238</doi><tpages>8</tpages><oa>free_for_read</oa></addata></record>
fulltext	fulltext
identifier	ISSN: 0033-569X
ispartof	Quarterly of applied mathematics, 1958-01, Vol.15 (4), p.420-427
issn	0033-569X 1552-4485
language	eng
recordid	cdi_crossref_primary_10_1090_qam_98238
source	JSTOR Mathematics and Statistics; American Mathematical Society Journals and Series; JSTOR Complete Journals; American Mathematical Society Publications (Freely Accessible); EZB Electronic Journals Library
subjects	Coefficients Cylindrical coordinates Integers Marital property Ordinary differential equations Power series Recurrence relations Research article
title	Solutions of the Helmholtz equation for a class of non-separable cylindrical and rotational coordinate systems
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-04T16%3A38%3A47IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Solutions%20of%20the%20Helmholtz%20equation%20for%20a%20class%20of%20non-separable%20cylindrical%20and%20rotational%20coordinate%20systems&rft.jtitle=Quarterly%20of%20applied%20mathematics&rft.au=Weston,%20Vaughan%20H.&rft.date=1958-01-01&rft.volume=15&rft.issue=4&rft.spage=420&rft.epage=427&rft.pages=420-427&rft.issn=0033-569X&rft.eissn=1552-4485&rft_id=info:doi/10.1090/qam/98238&rft_dat=%3Cjstor_cross%3E43634504%3C/jstor_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_jstor_id=43634504&rfr_iscdi=true