Lucas polynomials and power sums
The three - term recurrence x n + y n = (x + y) · (x n-1 + y n-1 ) - xy · (x n-2 + y n-2 ) allows to express x n + y n as a polynomial in the two variables x + y and xy. This polynomial is the bivariate Lucas polynomial. This identity is not as well known as it should be. It can be explained algebra...
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| creator | Tamm, Ulrich |
| description | The three - term recurrence x n + y n = (x + y) · (x n-1 + y n-1 ) - xy · (x n-2 + y n-2 ) allows to express x n + y n as a polynomial in the two variables x + y and xy. This polynomial is the bivariate Lucas polynomial. This identity is not as well known as it should be. It can be explained algebraically via the Girard - Waring formula, combinatorially via Lucas numbers and polynomials, and analytically as a special orthogonal polynomial. We shall briefly describe all these aspects and present an application from number theory. |
| doi_str_mv | 10.1109/ITA.2013.6503003 |
| format | Conference Proceeding |
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This polynomial is the bivariate Lucas polynomial. This identity is not as well known as it should be. It can be explained algebraically via the Girard - Waring formula, combinatorially via Lucas numbers and polynomials, and analytically as a special orthogonal polynomial. 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This polynomial is the bivariate Lucas polynomial. This identity is not as well known as it should be. It can be explained algebraically via the Girard - Waring formula, combinatorially via Lucas numbers and polynomials, and analytically as a special orthogonal polynomial. We shall briefly describe all these aspects and present an application from number theory.</description><subject>Chebyshev approximation</subject><subject>Chebyshev polynomials</subject><subject>Cryptography</subject><subject>Educational institutions</subject><subject>Encoding</subject><subject>Girard - Waring formula</subject><subject>Lucas polynomials</subject><subject>orthogonal polynomials</subject><subject>Polynomials</subject><subject>zeta function</subject><isbn>9781467346481</isbn><isbn>1467346489</isbn><isbn>1467346470</isbn><isbn>9781467346474</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2013</creationdate><recordtype>conference_proceeding</recordtype><sourceid>6IE</sourceid><sourceid>RIE</sourceid><recordid>eNo1j01Lw0AQhkdEUGvugpf8gcSZncnu5liKH4WAl9zLmp2FSNOWrEX67y1YTw_Pc3jhBXgkrImwfV73y9ogcW0bZES-gnsS61isOLyGonX-3z3dQpHzFyISGWFLd1B2xyHk8rDfnnb7aQzbXIZdPPuPzmU-TvkBbtK5anHhAvrXl371XnUfb-vVsqtGcs13ZYQ8xUbwMzSe0pBc5EFFLYpBsZy8N2ycoUikUdukPCRSJy6maBMv4OlvdlTVzWEepzCfNpdP_AvmpD3h</recordid><startdate>201302</startdate><enddate>201302</enddate><creator>Tamm, Ulrich</creator><general>IEEE</general><scope>6IE</scope><scope>6IL</scope><scope>CBEJK</scope><scope>RIE</scope><scope>RIL</scope></search><sort><creationdate>201302</creationdate><title>Lucas polynomials and power sums</title><author>Tamm, Ulrich</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-i175t-24181d540ba581fcf7d3ce4e60420463f88232721d11ede9fe3cf1e747dfd6f3</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Chebyshev approximation</topic><topic>Chebyshev polynomials</topic><topic>Cryptography</topic><topic>Educational institutions</topic><topic>Encoding</topic><topic>Girard - Waring formula</topic><topic>Lucas polynomials</topic><topic>orthogonal polynomials</topic><topic>Polynomials</topic><topic>zeta function</topic><toplevel>online_resources</toplevel><creatorcontrib>Tamm, Ulrich</creatorcontrib><collection>IEEE Electronic Library (IEL) Conference Proceedings</collection><collection>IEEE Proceedings Order Plan All Online (POP All Online) 1998-present by volume</collection><collection>IEEE Xplore All Conference Proceedings</collection><collection>IEEE Electronic Library (IEL)</collection><collection>IEEE Proceedings Order Plans (POP All) 1998-Present</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Tamm, Ulrich</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Lucas polynomials and power sums</atitle><btitle>2013 Information Theory and Applications Workshop (ITA)</btitle><stitle>ITA</stitle><date>2013-02</date><risdate>2013</risdate><spage>1</spage><epage>4</epage><pages>1-4</pages><isbn>9781467346481</isbn><isbn>1467346489</isbn><eisbn>1467346470</eisbn><eisbn>9781467346474</eisbn><abstract>The three - term recurrence x n + y n = (x + y) · (x n-1 + y n-1 ) - xy · (x n-2 + y n-2 ) allows to express x n + y n as a polynomial in the two variables x + y and xy. This polynomial is the bivariate Lucas polynomial. This identity is not as well known as it should be. It can be explained algebraically via the Girard - Waring formula, combinatorially via Lucas numbers and polynomials, and analytically as a special orthogonal polynomial. We shall briefly describe all these aspects and present an application from number theory.</abstract><pub>IEEE</pub><doi>10.1109/ITA.2013.6503003</doi><tpages>4</tpages></addata></record> |
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| language | eng |
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| source | IEEE Electronic Library (IEL) Conference Proceedings |
| subjects | Chebyshev approximation Chebyshev polynomials Cryptography Educational institutions Encoding Girard - Waring formula Lucas polynomials orthogonal polynomials Polynomials zeta function |
| title | Lucas polynomials and power sums |
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