Several q-series transformation formulas and new Hecke–Rogers type series identities
Abstract In this paper, we establish a general q-series expansion formula based on Bailey’s summation formula, whose limiting form reduces to the q-series expansion formula due to Wang and Chern (Integral Transform Special Funct 31(11):873–890, 2020). As applications, four q-series transformations a...
Ausführliche Beschreibung
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| Autor*in: |
Zhang, Ying [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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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. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Übergeordnetes Werk: |
Enthalten in: The Ramanujan journal - Springer US, 1997, 60(2023), 3 vom: 27. Jan., Seite 627-657 |
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| Übergeordnetes Werk: |
volume:60 ; year:2023 ; number:3 ; day:27 ; month:01 ; pages:627-657 |
| Links: |
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| DOI / URN: |
10.1007/s11139-022-00645-6 |
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OLC2134162783 |
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10.1007/s11139-022-00645-6 doi (DE-627)OLC2134162783 (DE-He213)s11139-022-00645-6-p DE-627 ger DE-627 rakwb eng 510 VZ 7,24 ssgn Zhang, Ying verfasserin aut Several q-series transformation formulas and new Hecke–Rogers type series identities 2023 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. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we establish a general q-series expansion formula based on Bailey’s summation formula, whose limiting form reduces to the q-series expansion formula due to Wang and Chern (Integral Transform Special Funct 31(11):873–890, 2020). As applications, four q-series transformations are derived, which imply numerous new Hecke–Rogers type series representations for Eulerian form series and double sums, especially involving the special cases of several q-orthogonal polynomials. Hecke–Rogers type series Bailey’s formula Watson’s -Whipple transformation formula -Orthogonal polynomials Zhang, Wenlong aut Zhang, Jingjing aut Enthalten in The Ramanujan journal Springer US, 1997 60(2023), 3 vom: 27. Jan., Seite 627-657 (DE-627)234141301 (DE-600)1394097-1 (DE-576)100004989 1382-4090 nnns volume:60 year:2023 number:3 day:27 month:01 pages:627-657 https://doi.org/10.1007/s11139-022-00645-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT SSG-OPC-ANG AR 60 2023 3 27 01 627-657 |
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10.1007/s11139-022-00645-6 doi (DE-627)OLC2134162783 (DE-He213)s11139-022-00645-6-p DE-627 ger DE-627 rakwb eng 510 VZ 7,24 ssgn Zhang, Ying verfasserin aut Several q-series transformation formulas and new Hecke–Rogers type series identities 2023 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. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we establish a general q-series expansion formula based on Bailey’s summation formula, whose limiting form reduces to the q-series expansion formula due to Wang and Chern (Integral Transform Special Funct 31(11):873–890, 2020). As applications, four q-series transformations are derived, which imply numerous new Hecke–Rogers type series representations for Eulerian form series and double sums, especially involving the special cases of several q-orthogonal polynomials. Hecke–Rogers type series Bailey’s formula Watson’s -Whipple transformation formula -Orthogonal polynomials Zhang, Wenlong aut Zhang, Jingjing aut Enthalten in The Ramanujan journal Springer US, 1997 60(2023), 3 vom: 27. Jan., Seite 627-657 (DE-627)234141301 (DE-600)1394097-1 (DE-576)100004989 1382-4090 nnns volume:60 year:2023 number:3 day:27 month:01 pages:627-657 https://doi.org/10.1007/s11139-022-00645-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT SSG-OPC-ANG AR 60 2023 3 27 01 627-657 |
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10.1007/s11139-022-00645-6 doi (DE-627)OLC2134162783 (DE-He213)s11139-022-00645-6-p DE-627 ger DE-627 rakwb eng 510 VZ 7,24 ssgn Zhang, Ying verfasserin aut Several q-series transformation formulas and new Hecke–Rogers type series identities 2023 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. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we establish a general q-series expansion formula based on Bailey’s summation formula, whose limiting form reduces to the q-series expansion formula due to Wang and Chern (Integral Transform Special Funct 31(11):873–890, 2020). As applications, four q-series transformations are derived, which imply numerous new Hecke–Rogers type series representations for Eulerian form series and double sums, especially involving the special cases of several q-orthogonal polynomials. Hecke–Rogers type series Bailey’s formula Watson’s -Whipple transformation formula -Orthogonal polynomials Zhang, Wenlong aut Zhang, Jingjing aut Enthalten in The Ramanujan journal Springer US, 1997 60(2023), 3 vom: 27. Jan., Seite 627-657 (DE-627)234141301 (DE-600)1394097-1 (DE-576)100004989 1382-4090 nnns volume:60 year:2023 number:3 day:27 month:01 pages:627-657 https://doi.org/10.1007/s11139-022-00645-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT SSG-OPC-ANG AR 60 2023 3 27 01 627-657 |
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10.1007/s11139-022-00645-6 doi (DE-627)OLC2134162783 (DE-He213)s11139-022-00645-6-p DE-627 ger DE-627 rakwb eng 510 VZ 7,24 ssgn Zhang, Ying verfasserin aut Several q-series transformation formulas and new Hecke–Rogers type series identities 2023 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. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we establish a general q-series expansion formula based on Bailey’s summation formula, whose limiting form reduces to the q-series expansion formula due to Wang and Chern (Integral Transform Special Funct 31(11):873–890, 2020). As applications, four q-series transformations are derived, which imply numerous new Hecke–Rogers type series representations for Eulerian form series and double sums, especially involving the special cases of several q-orthogonal polynomials. Hecke–Rogers type series Bailey’s formula Watson’s -Whipple transformation formula -Orthogonal polynomials Zhang, Wenlong aut Zhang, Jingjing aut Enthalten in The Ramanujan journal Springer US, 1997 60(2023), 3 vom: 27. Jan., Seite 627-657 (DE-627)234141301 (DE-600)1394097-1 (DE-576)100004989 1382-4090 nnns volume:60 year:2023 number:3 day:27 month:01 pages:627-657 https://doi.org/10.1007/s11139-022-00645-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT SSG-OPC-ANG AR 60 2023 3 27 01 627-657 |
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10.1007/s11139-022-00645-6 doi (DE-627)OLC2134162783 (DE-He213)s11139-022-00645-6-p DE-627 ger DE-627 rakwb eng 510 VZ 7,24 ssgn Zhang, Ying verfasserin aut Several q-series transformation formulas and new Hecke–Rogers type series identities 2023 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. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we establish a general q-series expansion formula based on Bailey’s summation formula, whose limiting form reduces to the q-series expansion formula due to Wang and Chern (Integral Transform Special Funct 31(11):873–890, 2020). As applications, four q-series transformations are derived, which imply numerous new Hecke–Rogers type series representations for Eulerian form series and double sums, especially involving the special cases of several q-orthogonal polynomials. Hecke–Rogers type series Bailey’s formula Watson’s -Whipple transformation formula -Orthogonal polynomials Zhang, Wenlong aut Zhang, Jingjing aut Enthalten in The Ramanujan journal Springer US, 1997 60(2023), 3 vom: 27. Jan., Seite 627-657 (DE-627)234141301 (DE-600)1394097-1 (DE-576)100004989 1382-4090 nnns volume:60 year:2023 number:3 day:27 month:01 pages:627-657 https://doi.org/10.1007/s11139-022-00645-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT SSG-OPC-ANG AR 60 2023 3 27 01 627-657 |
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Abstract In this paper, we establish a general q-series expansion formula based on Bailey’s summation formula, whose limiting form reduces to the q-series expansion formula due to Wang and Chern (Integral Transform Special Funct 31(11):873–890, 2020). As applications, four q-series transformations are derived, which imply numerous new Hecke–Rogers type series representations for Eulerian form series and double sums, especially involving the special cases of several q-orthogonal polynomials. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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Abstract In this paper, we establish a general q-series expansion formula based on Bailey’s summation formula, whose limiting form reduces to the q-series expansion formula due to Wang and Chern (Integral Transform Special Funct 31(11):873–890, 2020). As applications, four q-series transformations are derived, which imply numerous new Hecke–Rogers type series representations for Eulerian form series and double sums, especially involving the special cases of several q-orthogonal polynomials. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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Abstract In this paper, we establish a general q-series expansion formula based on Bailey’s summation formula, whose limiting form reduces to the q-series expansion formula due to Wang and Chern (Integral Transform Special Funct 31(11):873–890, 2020). As applications, four q-series transformations are derived, which imply numerous new Hecke–Rogers type series representations for Eulerian form series and double sums, especially involving the special cases of several q-orthogonal polynomials. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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10.1007/s11139-022-00645-6 |
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2024-07-03T23:45:57.768Z |
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Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, we establish a general q-series expansion formula based on Bailey’s summation formula, whose limiting form reduces to the q-series expansion formula due to Wang and Chern (Integral Transform Special Funct 31(11):873–890, 2020). 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