Dyson’s “Favorite” Identity and Chebyshev Polynomials of the Third and Fourth Kind
The combinatorial and analytic properties of Dyson’s “favorite” identity are studied in detail. In particular, a q -series analog of the anti-telescoping method is used to provide a new proof of Dyson’s results with mock theta functions popping up in intermediate steps. This leads to the appearance...
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| Veröffentlicht in: | Annals of combinatorics 2019-11, Vol.23 (3-4), p.443-464 |
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| container_end_page | 464 |
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| container_issue | 3-4 |
| container_start_page | 443 |
| container_title | Annals of combinatorics |
| container_volume | 23 |
| creator | Andrews, George E. |
| description | The combinatorial and analytic properties of Dyson’s “favorite” identity are studied in detail. In particular, a
q
-series analog of the anti-telescoping method is used to provide a new proof of Dyson’s results with mock theta functions popping up in intermediate steps. This leads to the appearance of Chebyshev polynomials of the third and fourth kind in Bailey pairs related to Bailey’s Lemma. The natural relationship with L.J. Rogers’s pioneering work is also presented. |
| doi_str_mv | 10.1007/s00026-019-00443-w |
| format | Article |
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-series analog of the anti-telescoping method is used to provide a new proof of Dyson’s results with mock theta functions popping up in intermediate steps. This leads to the appearance of Chebyshev polynomials of the third and fourth kind in Bailey pairs related to Bailey’s Lemma. The natural relationship with L.J. Rogers’s pioneering work is also presented.</description><identifier>ISSN: 0218-0006</identifier><identifier>EISSN: 0219-3094</identifier><identifier>DOI: 10.1007/s00026-019-00443-w</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Chebyshev approximation ; Combinatorial analysis ; Combinatorics ; Ice ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Polynomials ; Telescoping</subject><ispartof>Annals of combinatorics, 2019-11, Vol.23 (3-4), p.443-464</ispartof><rights>Springer Nature Switzerland AG 2019</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-e31147b049fac4dfa792c848e682b3d58db4cc9b1b7847ecac068820299c68d53</citedby><cites>FETCH-LOGICAL-c319t-e31147b049fac4dfa792c848e682b3d58db4cc9b1b7847ecac068820299c68d53</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00026-019-00443-w$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00026-019-00443-w$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Andrews, George E.</creatorcontrib><title>Dyson’s “Favorite” Identity and Chebyshev Polynomials of the Third and Fourth Kind</title><title>Annals of combinatorics</title><addtitle>Ann. Comb</addtitle><description>The combinatorial and analytic properties of Dyson’s “favorite” identity are studied in detail. In particular, a
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-series analog of the anti-telescoping method is used to provide a new proof of Dyson’s results with mock theta functions popping up in intermediate steps. This leads to the appearance of Chebyshev polynomials of the third and fourth kind in Bailey pairs related to Bailey’s Lemma. The natural relationship with L.J. Rogers’s pioneering work is also presented.</description><subject>Chebyshev approximation</subject><subject>Combinatorial analysis</subject><subject>Combinatorics</subject><subject>Ice</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Polynomials</subject><subject>Telescoping</subject><issn>0218-0006</issn><issn>0219-3094</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9kM9KAzEQxoMoWKsv4CngeXXyp7vJUarVYkEPFbyF3STrbmk3Ndla9tbXEPTl-iTGVvDmab5hft_M8CF0TuCSAGRXAQBomgCRCQDnLFkfoB7Q2DKQ_HCnRRxBeoxOQphFlQGjPfRy0wXXbDcfAW83n6P83fm6tdvNFx4b27R12-G8MXhY2aILlX3HT27eNW5R5_OAXYnbyuJpVXuzw0Zu5dsKP9SNOUVHZWTs2W_to-fR7XR4n0we78bD60miGZFtYhkhPCuAyzLX3JR5JqkWXNhU0IKZgTAF11oWpMgEz6zONaRCUKBS6lSYAeuji_3epXdvKxtaNYtPNPGkooxSJmiWkkjRPaW9C8HbUi19vch9pwionwTVPkEVE1S7BNU6mtjeFCLcvFr_t_of1zd09Xai</recordid><startdate>20191101</startdate><enddate>20191101</enddate><creator>Andrews, George E.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20191101</creationdate><title>Dyson’s “Favorite” Identity and Chebyshev Polynomials of the Third and Fourth Kind</title><author>Andrews, George E.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-e31147b049fac4dfa792c848e682b3d58db4cc9b1b7847ecac068820299c68d53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Chebyshev approximation</topic><topic>Combinatorial analysis</topic><topic>Combinatorics</topic><topic>Ice</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Polynomials</topic><topic>Telescoping</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Andrews, George E.</creatorcontrib><collection>CrossRef</collection><jtitle>Annals of combinatorics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Andrews, George E.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dyson’s “Favorite” Identity and Chebyshev Polynomials of the Third and Fourth Kind</atitle><jtitle>Annals of combinatorics</jtitle><stitle>Ann. Comb</stitle><date>2019-11-01</date><risdate>2019</risdate><volume>23</volume><issue>3-4</issue><spage>443</spage><epage>464</epage><pages>443-464</pages><issn>0218-0006</issn><eissn>0219-3094</eissn><abstract>The combinatorial and analytic properties of Dyson’s “favorite” identity are studied in detail. In particular, a
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-series analog of the anti-telescoping method is used to provide a new proof of Dyson’s results with mock theta functions popping up in intermediate steps. This leads to the appearance of Chebyshev polynomials of the third and fourth kind in Bailey pairs related to Bailey’s Lemma. The natural relationship with L.J. Rogers’s pioneering work is also presented.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00026-019-00443-w</doi><tpages>22</tpages></addata></record> |
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| language | eng |
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| subjects | Chebyshev approximation Combinatorial analysis Combinatorics Ice Mathematical analysis Mathematics Mathematics and Statistics Polynomials Telescoping |
| title | Dyson’s “Favorite” Identity and Chebyshev Polynomials of the Third and Fourth Kind |
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