An expansion of %$(q, \lambda )%$-derivative operator
Abstract We give the concept of Generalized Rogers–Szegö polynomials based on the %$(q, \lambda )%$-derivative operator and %$(q, \mu )%$-derivative operator. Then we use the method of Liu’s calculus to obtain the expansion theorem involving Generalized Rogers–Szegö polynomials. In addition, we use...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Yang, Dunkun [verfasserIn] |
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| Format: |
E-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 - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997, 60(2022), 4 vom: 28. Okt., Seite 1127-1149 |
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| Übergeordnetes Werk: |
volume:60 ; year:2022 ; number:4 ; day:28 ; month:10 ; pages:1127-1149 |
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| DOI / URN: |
10.1007/s11139-022-00617-w |
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| Katalog-ID: |
SPR049799916 |
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| 520 | |a Abstract We give the concept of Generalized Rogers–Szegö polynomials based on the %$(q, \lambda )%$-derivative operator and %$(q, \mu )%$-derivative operator. Then we use the method of Liu’s calculus to obtain the expansion theorem involving Generalized Rogers–Szegö polynomials. In addition, we use two kinds of the %$(q, \lambda )%$-exponential functions and extend some identities of Zhang. At last, we consider the properties when %$\lambda =1%$ and %$\mu =1%$, and use the method of the generating functions and q-Mehler formula for Al-Salam–Carlitz polynomials to establish some new identities. | ||
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10.1007/s11139-022-00617-w doi (DE-627)SPR049799916 (SPR)s11139-022-00617-w-e DE-627 ger DE-627 rakwb eng Yang, Dunkun verfasserin (orcid)0000-0003-1024-6330 aut An expansion of %$(q, \lambda )%$-derivative operator 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We give the concept of Generalized Rogers–Szegö polynomials based on the %$(q, \lambda )%$-derivative operator and %$(q, \mu )%$-derivative operator. Then we use the method of Liu’s calculus to obtain the expansion theorem involving Generalized Rogers–Szegö polynomials. In addition, we use two kinds of the %$(q, \lambda )%$-exponential functions and extend some identities of Zhang. At last, we consider the properties when %$\lambda =1%$ and %$\mu =1%$, and use the method of the generating functions and q-Mehler formula for Al-Salam–Carlitz polynomials to establish some new identities. Liu’s calculus (dpeaa)DE-He213 -Differential operator (dpeaa)DE-He213 -Exponential operator (dpeaa)DE-He213 Enthalten in The Ramanujan journal Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 60(2022), 4 vom: 28. Okt., Seite 1127-1149 (DE-627)320521133 (DE-600)2014600-0 1572-9303 nnns volume:60 year:2022 number:4 day:28 month:10 pages:1127-1149 https://dx.doi.org/10.1007/s11139-022-00617-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 60 2022 4 28 10 1127-1149 |
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10.1007/s11139-022-00617-w doi (DE-627)SPR049799916 (SPR)s11139-022-00617-w-e DE-627 ger DE-627 rakwb eng Yang, Dunkun verfasserin (orcid)0000-0003-1024-6330 aut An expansion of %$(q, \lambda )%$-derivative operator 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We give the concept of Generalized Rogers–Szegö polynomials based on the %$(q, \lambda )%$-derivative operator and %$(q, \mu )%$-derivative operator. Then we use the method of Liu’s calculus to obtain the expansion theorem involving Generalized Rogers–Szegö polynomials. In addition, we use two kinds of the %$(q, \lambda )%$-exponential functions and extend some identities of Zhang. At last, we consider the properties when %$\lambda =1%$ and %$\mu =1%$, and use the method of the generating functions and q-Mehler formula for Al-Salam–Carlitz polynomials to establish some new identities. Liu’s calculus (dpeaa)DE-He213 -Differential operator (dpeaa)DE-He213 -Exponential operator (dpeaa)DE-He213 Enthalten in The Ramanujan journal Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 60(2022), 4 vom: 28. Okt., Seite 1127-1149 (DE-627)320521133 (DE-600)2014600-0 1572-9303 nnns volume:60 year:2022 number:4 day:28 month:10 pages:1127-1149 https://dx.doi.org/10.1007/s11139-022-00617-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 60 2022 4 28 10 1127-1149 |
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10.1007/s11139-022-00617-w doi (DE-627)SPR049799916 (SPR)s11139-022-00617-w-e DE-627 ger DE-627 rakwb eng Yang, Dunkun verfasserin (orcid)0000-0003-1024-6330 aut An expansion of %$(q, \lambda )%$-derivative operator 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We give the concept of Generalized Rogers–Szegö polynomials based on the %$(q, \lambda )%$-derivative operator and %$(q, \mu )%$-derivative operator. Then we use the method of Liu’s calculus to obtain the expansion theorem involving Generalized Rogers–Szegö polynomials. In addition, we use two kinds of the %$(q, \lambda )%$-exponential functions and extend some identities of Zhang. At last, we consider the properties when %$\lambda =1%$ and %$\mu =1%$, and use the method of the generating functions and q-Mehler formula for Al-Salam–Carlitz polynomials to establish some new identities. Liu’s calculus (dpeaa)DE-He213 -Differential operator (dpeaa)DE-He213 -Exponential operator (dpeaa)DE-He213 Enthalten in The Ramanujan journal Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 60(2022), 4 vom: 28. Okt., Seite 1127-1149 (DE-627)320521133 (DE-600)2014600-0 1572-9303 nnns volume:60 year:2022 number:4 day:28 month:10 pages:1127-1149 https://dx.doi.org/10.1007/s11139-022-00617-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 60 2022 4 28 10 1127-1149 |
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10.1007/s11139-022-00617-w doi (DE-627)SPR049799916 (SPR)s11139-022-00617-w-e DE-627 ger DE-627 rakwb eng Yang, Dunkun verfasserin (orcid)0000-0003-1024-6330 aut An expansion of %$(q, \lambda )%$-derivative operator 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We give the concept of Generalized Rogers–Szegö polynomials based on the %$(q, \lambda )%$-derivative operator and %$(q, \mu )%$-derivative operator. Then we use the method of Liu’s calculus to obtain the expansion theorem involving Generalized Rogers–Szegö polynomials. In addition, we use two kinds of the %$(q, \lambda )%$-exponential functions and extend some identities of Zhang. At last, we consider the properties when %$\lambda =1%$ and %$\mu =1%$, and use the method of the generating functions and q-Mehler formula for Al-Salam–Carlitz polynomials to establish some new identities. Liu’s calculus (dpeaa)DE-He213 -Differential operator (dpeaa)DE-He213 -Exponential operator (dpeaa)DE-He213 Enthalten in The Ramanujan journal Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 60(2022), 4 vom: 28. Okt., Seite 1127-1149 (DE-627)320521133 (DE-600)2014600-0 1572-9303 nnns volume:60 year:2022 number:4 day:28 month:10 pages:1127-1149 https://dx.doi.org/10.1007/s11139-022-00617-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 60 2022 4 28 10 1127-1149 |
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10.1007/s11139-022-00617-w doi (DE-627)SPR049799916 (SPR)s11139-022-00617-w-e DE-627 ger DE-627 rakwb eng Yang, Dunkun verfasserin (orcid)0000-0003-1024-6330 aut An expansion of %$(q, \lambda )%$-derivative operator 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We give the concept of Generalized Rogers–Szegö polynomials based on the %$(q, \lambda )%$-derivative operator and %$(q, \mu )%$-derivative operator. Then we use the method of Liu’s calculus to obtain the expansion theorem involving Generalized Rogers–Szegö polynomials. In addition, we use two kinds of the %$(q, \lambda )%$-exponential functions and extend some identities of Zhang. At last, we consider the properties when %$\lambda =1%$ and %$\mu =1%$, and use the method of the generating functions and q-Mehler formula for Al-Salam–Carlitz polynomials to establish some new identities. Liu’s calculus (dpeaa)DE-He213 -Differential operator (dpeaa)DE-He213 -Exponential operator (dpeaa)DE-He213 Enthalten in The Ramanujan journal Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 60(2022), 4 vom: 28. Okt., Seite 1127-1149 (DE-627)320521133 (DE-600)2014600-0 1572-9303 nnns volume:60 year:2022 number:4 day:28 month:10 pages:1127-1149 https://dx.doi.org/10.1007/s11139-022-00617-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 60 2022 4 28 10 1127-1149 |
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Abstract We give the concept of Generalized Rogers–Szegö polynomials based on the %$(q, \lambda )%$-derivative operator and %$(q, \mu )%$-derivative operator. Then we use the method of Liu’s calculus to obtain the expansion theorem involving Generalized Rogers–Szegö polynomials. In addition, we use two kinds of the %$(q, \lambda )%$-exponential functions and extend some identities of Zhang. At last, we consider the properties when %$\lambda =1%$ and %$\mu =1%$, and use the method of the generating functions and q-Mehler formula for Al-Salam–Carlitz polynomials to establish some new identities. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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Abstract We give the concept of Generalized Rogers–Szegö polynomials based on the %$(q, \lambda )%$-derivative operator and %$(q, \mu )%$-derivative operator. Then we use the method of Liu’s calculus to obtain the expansion theorem involving Generalized Rogers–Szegö polynomials. In addition, we use two kinds of the %$(q, \lambda )%$-exponential functions and extend some identities of Zhang. At last, we consider the properties when %$\lambda =1%$ and %$\mu =1%$, and use the method of the generating functions and q-Mehler formula for Al-Salam–Carlitz polynomials to establish some new identities. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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Abstract We give the concept of Generalized Rogers–Szegö polynomials based on the %$(q, \lambda )%$-derivative operator and %$(q, \mu )%$-derivative operator. Then we use the method of Liu’s calculus to obtain the expansion theorem involving Generalized Rogers–Szegö polynomials. In addition, we use two kinds of the %$(q, \lambda )%$-exponential functions and extend some identities of Zhang. At last, we consider the properties when %$\lambda =1%$ and %$\mu =1%$, and use the method of the generating functions and q-Mehler formula for Al-Salam–Carlitz polynomials to establish some new identities. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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