Rogers–Ramanujan type identities and Chebyshev polynomials of the third kind
Abstract It is known that q-orthogonal polynomials play an important role in the field of q-series and special functions. While studying Dyson’s “favorite” identity of Rogers–Ramanujan type, Andrews pointed out that the classical orthogonal polynomials also have surprising applications in the world...
Ausführliche Beschreibung
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| Autor*in: |
Sun, Lisa H. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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| Übergeordnetes Werk: |
Enthalten in: The Ramanujan journal - Springer US, 1997, 60(2022), 3 vom: 27. Okt., Seite 761-794 |
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| Übergeordnetes Werk: |
volume:60 ; year:2022 ; number:3 ; day:27 ; month:10 ; pages:761-794 |
| Links: |
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| DOI / URN: |
10.1007/s11139-022-00627-8 |
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| 520 | |a Abstract It is known that q-orthogonal polynomials play an important role in the field of q-series and special functions. While studying Dyson’s “favorite” identity of Rogers–Ramanujan type, Andrews pointed out that the classical orthogonal polynomials also have surprising applications in the world of q. By introducing Chebyshev polynomials of the third and the fourth kinds into Bailey pairs, Andrews derived a family of Rogers–Ramanujan type identities and also results related to mock theta functions and Hecke-type series. In this paper, by constructing a new Bailey pair involving Chebyshev polynomials of the third kind, we further extend Andrews’ way of studying Rogers-Ramanujan type identities. By inserting this Bailey pair into various weak forms of Bailey’s lemma, we obtain a companion identity for Dyson’s favorite identity and a number of Rogers–Ramanujan type identities. As a consequences, we also obtain results related to Appell–Lerch series and the generalized Hecke-type series. Furthermore, our key Bailey pair also fits in the bilateral versions of Bailey’s lemma due to Andrews and Warnaar, which leads to more identities for the generalized Hecke-type series and false theta functions. | ||
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| 650 | 4 | |a Hecke-type series | |
| 650 | 4 | |a False theta functions | |
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10.1007/s11139-022-00627-8 doi (DE-627)OLC2134162740 (DE-He213)s11139-022-00627-8-p DE-627 ger DE-627 rakwb eng 510 VZ 7,24 ssgn Sun, Lisa H. verfasserin (orcid)0000-0002-0901-9539 aut Rogers–Ramanujan type identities and Chebyshev polynomials of the third kind 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract It is known that q-orthogonal polynomials play an important role in the field of q-series and special functions. While studying Dyson’s “favorite” identity of Rogers–Ramanujan type, Andrews pointed out that the classical orthogonal polynomials also have surprising applications in the world of q. By introducing Chebyshev polynomials of the third and the fourth kinds into Bailey pairs, Andrews derived a family of Rogers–Ramanujan type identities and also results related to mock theta functions and Hecke-type series. In this paper, by constructing a new Bailey pair involving Chebyshev polynomials of the third kind, we further extend Andrews’ way of studying Rogers-Ramanujan type identities. By inserting this Bailey pair into various weak forms of Bailey’s lemma, we obtain a companion identity for Dyson’s favorite identity and a number of Rogers–Ramanujan type identities. As a consequences, we also obtain results related to Appell–Lerch series and the generalized Hecke-type series. Furthermore, our key Bailey pair also fits in the bilateral versions of Bailey’s lemma due to Andrews and Warnaar, which leads to more identities for the generalized Hecke-type series and false theta functions. Rogers–Ramanujan type identities Dyson’s favorite identity Bailey pair Bailey’s lemma Chebyshev polynomials Appell–Lerch series Hecke-type series False theta functions Enthalten in The Ramanujan journal Springer US, 1997 60(2022), 3 vom: 27. Okt., Seite 761-794 (DE-627)234141301 (DE-600)1394097-1 (DE-576)100004989 1382-4090 nnns volume:60 year:2022 number:3 day:27 month:10 pages:761-794 https://doi.org/10.1007/s11139-022-00627-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT SSG-OPC-ANG AR 60 2022 3 27 10 761-794 |
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10.1007/s11139-022-00627-8 doi (DE-627)OLC2134162740 (DE-He213)s11139-022-00627-8-p DE-627 ger DE-627 rakwb eng 510 VZ 7,24 ssgn Sun, Lisa H. verfasserin (orcid)0000-0002-0901-9539 aut Rogers–Ramanujan type identities and Chebyshev polynomials of the third kind 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract It is known that q-orthogonal polynomials play an important role in the field of q-series and special functions. While studying Dyson’s “favorite” identity of Rogers–Ramanujan type, Andrews pointed out that the classical orthogonal polynomials also have surprising applications in the world of q. By introducing Chebyshev polynomials of the third and the fourth kinds into Bailey pairs, Andrews derived a family of Rogers–Ramanujan type identities and also results related to mock theta functions and Hecke-type series. In this paper, by constructing a new Bailey pair involving Chebyshev polynomials of the third kind, we further extend Andrews’ way of studying Rogers-Ramanujan type identities. By inserting this Bailey pair into various weak forms of Bailey’s lemma, we obtain a companion identity for Dyson’s favorite identity and a number of Rogers–Ramanujan type identities. As a consequences, we also obtain results related to Appell–Lerch series and the generalized Hecke-type series. Furthermore, our key Bailey pair also fits in the bilateral versions of Bailey’s lemma due to Andrews and Warnaar, which leads to more identities for the generalized Hecke-type series and false theta functions. Rogers–Ramanujan type identities Dyson’s favorite identity Bailey pair Bailey’s lemma Chebyshev polynomials Appell–Lerch series Hecke-type series False theta functions Enthalten in The Ramanujan journal Springer US, 1997 60(2022), 3 vom: 27. Okt., Seite 761-794 (DE-627)234141301 (DE-600)1394097-1 (DE-576)100004989 1382-4090 nnns volume:60 year:2022 number:3 day:27 month:10 pages:761-794 https://doi.org/10.1007/s11139-022-00627-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT SSG-OPC-ANG AR 60 2022 3 27 10 761-794 |
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10.1007/s11139-022-00627-8 doi (DE-627)OLC2134162740 (DE-He213)s11139-022-00627-8-p DE-627 ger DE-627 rakwb eng 510 VZ 7,24 ssgn Sun, Lisa H. verfasserin (orcid)0000-0002-0901-9539 aut Rogers–Ramanujan type identities and Chebyshev polynomials of the third kind 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract It is known that q-orthogonal polynomials play an important role in the field of q-series and special functions. While studying Dyson’s “favorite” identity of Rogers–Ramanujan type, Andrews pointed out that the classical orthogonal polynomials also have surprising applications in the world of q. By introducing Chebyshev polynomials of the third and the fourth kinds into Bailey pairs, Andrews derived a family of Rogers–Ramanujan type identities and also results related to mock theta functions and Hecke-type series. In this paper, by constructing a new Bailey pair involving Chebyshev polynomials of the third kind, we further extend Andrews’ way of studying Rogers-Ramanujan type identities. By inserting this Bailey pair into various weak forms of Bailey’s lemma, we obtain a companion identity for Dyson’s favorite identity and a number of Rogers–Ramanujan type identities. As a consequences, we also obtain results related to Appell–Lerch series and the generalized Hecke-type series. Furthermore, our key Bailey pair also fits in the bilateral versions of Bailey’s lemma due to Andrews and Warnaar, which leads to more identities for the generalized Hecke-type series and false theta functions. Rogers–Ramanujan type identities Dyson’s favorite identity Bailey pair Bailey’s lemma Chebyshev polynomials Appell–Lerch series Hecke-type series False theta functions Enthalten in The Ramanujan journal Springer US, 1997 60(2022), 3 vom: 27. Okt., Seite 761-794 (DE-627)234141301 (DE-600)1394097-1 (DE-576)100004989 1382-4090 nnns volume:60 year:2022 number:3 day:27 month:10 pages:761-794 https://doi.org/10.1007/s11139-022-00627-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT SSG-OPC-ANG AR 60 2022 3 27 10 761-794 |
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rogers–ramanujan type identities and chebyshev polynomials of the third kind |
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Rogers–Ramanujan type identities and Chebyshev polynomials of the third kind |
| abstract |
Abstract It is known that q-orthogonal polynomials play an important role in the field of q-series and special functions. While studying Dyson’s “favorite” identity of Rogers–Ramanujan type, Andrews pointed out that the classical orthogonal polynomials also have surprising applications in the world of q. By introducing Chebyshev polynomials of the third and the fourth kinds into Bailey pairs, Andrews derived a family of Rogers–Ramanujan type identities and also results related to mock theta functions and Hecke-type series. In this paper, by constructing a new Bailey pair involving Chebyshev polynomials of the third kind, we further extend Andrews’ way of studying Rogers-Ramanujan type identities. By inserting this Bailey pair into various weak forms of Bailey’s lemma, we obtain a companion identity for Dyson’s favorite identity and a number of Rogers–Ramanujan type identities. As a consequences, we also obtain results related to Appell–Lerch series and the generalized Hecke-type series. Furthermore, our key Bailey pair also fits in the bilateral versions of Bailey’s lemma due to Andrews and Warnaar, which leads to more identities for the generalized Hecke-type series and false theta functions. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
| abstractGer |
Abstract It is known that q-orthogonal polynomials play an important role in the field of q-series and special functions. While studying Dyson’s “favorite” identity of Rogers–Ramanujan type, Andrews pointed out that the classical orthogonal polynomials also have surprising applications in the world of q. By introducing Chebyshev polynomials of the third and the fourth kinds into Bailey pairs, Andrews derived a family of Rogers–Ramanujan type identities and also results related to mock theta functions and Hecke-type series. In this paper, by constructing a new Bailey pair involving Chebyshev polynomials of the third kind, we further extend Andrews’ way of studying Rogers-Ramanujan type identities. By inserting this Bailey pair into various weak forms of Bailey’s lemma, we obtain a companion identity for Dyson’s favorite identity and a number of Rogers–Ramanujan type identities. As a consequences, we also obtain results related to Appell–Lerch series and the generalized Hecke-type series. Furthermore, our key Bailey pair also fits in the bilateral versions of Bailey’s lemma due to Andrews and Warnaar, which leads to more identities for the generalized Hecke-type series and false theta functions. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
| abstract_unstemmed |
Abstract It is known that q-orthogonal polynomials play an important role in the field of q-series and special functions. While studying Dyson’s “favorite” identity of Rogers–Ramanujan type, Andrews pointed out that the classical orthogonal polynomials also have surprising applications in the world of q. By introducing Chebyshev polynomials of the third and the fourth kinds into Bailey pairs, Andrews derived a family of Rogers–Ramanujan type identities and also results related to mock theta functions and Hecke-type series. In this paper, by constructing a new Bailey pair involving Chebyshev polynomials of the third kind, we further extend Andrews’ way of studying Rogers-Ramanujan type identities. By inserting this Bailey pair into various weak forms of Bailey’s lemma, we obtain a companion identity for Dyson’s favorite identity and a number of Rogers–Ramanujan type identities. As a consequences, we also obtain results related to Appell–Lerch series and the generalized Hecke-type series. Furthermore, our key Bailey pair also fits in the bilateral versions of Bailey’s lemma due to Andrews and Warnaar, which leads to more identities for the generalized Hecke-type series and false theta functions. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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Rogers–Ramanujan type identities and Chebyshev polynomials of the third kind |
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