Generalizations of Rogers–Ramanujan type identities Generalizations of Rogers–Ramanujan type identities
The Rogers–Ramanujan identities were first proved by Rogers in 1894 and later rediscovered by Ramanujan around 1913. During the study of these two identities, many Rogers–Ramanujan type identities have been found, and these identities have always been of great interest to mathematicians. In this pap...
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| Veröffentlicht in: | The Ramanujan journal Jg. 68; H. 1; S. 32 |
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| Abstract | The Rogers–Ramanujan identities were first proved by Rogers in 1894 and later rediscovered by Ramanujan around 1913. During the study of these two identities, many Rogers–Ramanujan type identities have been found, and these identities have always been of great interest to mathematicians. In this paper, by means of properties of Appell–Lerch sums in combination with Bailey pairs and Bailey’s lemma, we derive some generalizations of Rogers–Ramanujan type identities, which include some known identities and also imply some new ones. |
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| AbstractList | The Rogers–Ramanujan identities were first proved by Rogers in 1894 and later rediscovered by Ramanujan around 1913. During the study of these two identities, many Rogers–Ramanujan type identities have been found, and these identities have always been of great interest to mathematicians. In this paper, by means of properties of Appell–Lerch sums in combination with Bailey pairs and Bailey’s lemma, we derive some generalizations of Rogers–Ramanujan type identities, which include some known identities and also imply some new ones. |
| ArticleNumber | 32 |
| Author | Gu, Nancy S. S. Wang, Qian Cui, Su-Ping |
| Author_xml | – sequence: 1 givenname: Su-Ping surname: Cui fullname: Cui, Su-Ping organization: School of Mathematical Sciences, Qufu Normal University – sequence: 2 givenname: Nancy S. S. surname: Gu fullname: Gu, Nancy S. S. email: gu@nankai.edu.cn organization: Center for Combinatorics, LPMC, Nankai University – sequence: 3 givenname: Qian surname: Wang fullname: Wang, Qian organization: Center for Combinatorics, LPMC, Nankai University |
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| Cites_doi | 10.1016/j.aim.2020.107037 10.1017/CBO9780511526251 10.1017/S0017089516000197 10.1007/s00026-012-0148-3 10.1016/j.aam.2015.02.001 10.1112/plms/s2-53.6.460 10.1090/cbms/066 10.1090/btran/158 10.1007/s11139-006-8483-9 10.1016/j.jmaa.2008.03.033 10.1017/S0013091515000425 10.1016/j.aam.2021.102267 10.1112/plms/s2-50.1.1 10.37236/36 10.1016/j.aim.2014.07.018 10.1016/j.aam.2016.04.003 10.1016/j.jmaa.2022.126459 10.1007/s11139-007-9109-6 10.1016/j.aam.2008.07.003 10.2307/2372962 10.1142/S1793042106000401 10.1007/s00208-016-1390-5 10.37236/1706 10.1112/plms/pdu007 10.1112/plms/s2-54.2.147 10.1016/0097-3165(79)90008-6 10.4064/aa-43-2-155-166 10.1016/j.aam.2022.102347 10.2140/pjm.1984.114.267 10.1006/aama.1999.0658 10.1016/j.aam.2010.01.002 |
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| References | NSS Gu (1174_CR17) 2016; 79 LJ Slater (1174_CR36) 1952; 54 S-P Cui (1174_CR12) 2022; 515 DM Bressoud (1174_CR7) 1979; 27 KQ Ji (1174_CR21) 2015; 65 WN Bailey (1174_CR4) 1947; 49 DR Hickerson (1174_CR20) 2017; 367 NSS Gu (1174_CR18) 2010; 45 1174_CR26 G Gasper (1174_CR15) 2004 AV Sills (1174_CR33) 2006; 11 MJ Schlosser (1174_CR31) 2023; 10 LJ Slater (1174_CR35) 1951; 53 S Ramanujan (1174_CR29) 1914; 6 S-P Cui (1174_CR13) 2023; 151 W Chu (1174_CR9) 2009; 42 B Gordon (1174_CR16) 1961; 83 J McLaughlin (1174_CR24) 2008; 344 J McLaughlin (1174_CR25) 2012; 16 AV Sills (1174_CR34) 2018 GE Andrews (1174_CR3) 2009 JH Loxton (1174_CR23) 1984; 43 S-P Cui (1174_CR11) 2021; 131 S Cooper (1174_CR10) 2006; 2 OXM Yao (1174_CR37) 2022; 138 J Lovejoy (1174_CR22) 2017; 59 LJ Rogers (1174_CR30) 1894; 25 D Bowman (1174_CR6) 2009; 18 DR Hickerson (1174_CR19) 2014; 109 1174_CR2 1174_CR32 GE Andrews (1174_CR1) 1984; 114 D Chen (1174_CR8) 2020; 365 K Garrett (1174_CR14) 1999; 23 ET Mortenson (1174_CR28) 2016; 59 ET Mortenson (1174_CR27) 2014; 264 WN Bailey (1174_CR5) 1948; 50 |
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| SubjectTerms | Combinatorics Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Mathematics Mathematics and Statistics Number Theory |
| Subtitle | Generalizations of Rogers–Ramanujan type identities |
| Title | Generalizations of Rogers–Ramanujan type identities |
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