On Coefficients Problems for Typically Real Functions Related to Gegenbauer Polynomials
Abstract We solve problems concerning the coefficients of functions in the class %$\mathcal {T}(\lambda )%$ of typically real functions associated with Gegenbauer polynomials. The main aim is to determine the estimates of two expressions: %$|a_4-a_2 a_3|%$ and %$|a_2 a_4 -a_3{}^2|%$. The second one...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Zaprawa, Paweł [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) 2017 |
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| Übergeordnetes Werk: |
Enthalten in: Mediterranean journal of mathematics - Basel : Birkhäuser, 2004, 14(2017), 2 vom: 02. März |
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| Übergeordnetes Werk: |
volume:14 ; year:2017 ; number:2 ; day:02 ; month:03 |
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| DOI / URN: |
10.1007/s00009-017-0863-4 |
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| Katalog-ID: |
SPR000127841 |
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| 100 | 1 | |a Zaprawa, Paweł |e verfasserin |0 (orcid)0000-0002-7279-9582 |4 aut | |
| 245 | 1 | 0 | |a On Coefficients Problems for Typically Real Functions Related to Gegenbauer Polynomials |
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| 520 | |a Abstract We solve problems concerning the coefficients of functions in the class %$\mathcal {T}(\lambda )%$ of typically real functions associated with Gegenbauer polynomials. The main aim is to determine the estimates of two expressions: %$|a_4-a_2 a_3|%$ and %$|a_2 a_4 -a_3{}^2|%$. The second one is known as the second Hankel determinant. In order to obtain these bounds, we consider the regions of variability of selected pairs of coefficients for functions in %$\mathcal {T}(\lambda )%$. Furthermore, we find the upper and the lower bounds of functionals of Fekete–Szegö type. Finally, we present some conclusions for the classes %$\mathcal {T}%$ and %$\mathcal {T}(1/2)%$. | ||
| 650 | 4 | |a Gegenbauer polynomials |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a typically real functions |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a coefficient problems |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Hankel determinants |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Figiel, Magdalena |4 aut | |
| 700 | 1 | |a Futa, Anna |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Mediterranean journal of mathematics |d Basel : Birkhäuser, 2004 |g 14(2017), 2 vom: 02. März |w (DE-627)394566831 |w (DE-600)2160803-9 |x 1660-5454 |7 nnns |
| 773 | 1 | 8 | |g volume:14 |g year:2017 |g number:2 |g day:02 |g month:03 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s00009-017-0863-4 |z kostenfrei |3 Volltext |
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10.1007/s00009-017-0863-4 doi (DE-627)SPR000127841 (SPR)s00009-017-0863-4-e DE-627 ger DE-627 rakwb eng Zaprawa, Paweł verfasserin (orcid)0000-0002-7279-9582 aut On Coefficients Problems for Typically Real Functions Related to Gegenbauer Polynomials 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2017 Abstract We solve problems concerning the coefficients of functions in the class %$\mathcal {T}(\lambda )%$ of typically real functions associated with Gegenbauer polynomials. The main aim is to determine the estimates of two expressions: %$|a_4-a_2 a_3|%$ and %$|a_2 a_4 -a_3{}^2|%$. The second one is known as the second Hankel determinant. In order to obtain these bounds, we consider the regions of variability of selected pairs of coefficients for functions in %$\mathcal {T}(\lambda )%$. Furthermore, we find the upper and the lower bounds of functionals of Fekete–Szegö type. Finally, we present some conclusions for the classes %$\mathcal {T}%$ and %$\mathcal {T}(1/2)%$. Gegenbauer polynomials (dpeaa)DE-He213 typically real functions (dpeaa)DE-He213 coefficient problems (dpeaa)DE-He213 Hankel determinants (dpeaa)DE-He213 Figiel, Magdalena aut Futa, Anna aut Enthalten in Mediterranean journal of mathematics Basel : Birkhäuser, 2004 14(2017), 2 vom: 02. März (DE-627)394566831 (DE-600)2160803-9 1660-5454 nnns volume:14 year:2017 number:2 day:02 month:03 https://dx.doi.org/10.1007/s00009-017-0863-4 kostenfrei 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_65 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_267 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 14 2017 2 02 03 |
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10.1007/s00009-017-0863-4 doi (DE-627)SPR000127841 (SPR)s00009-017-0863-4-e DE-627 ger DE-627 rakwb eng Zaprawa, Paweł verfasserin (orcid)0000-0002-7279-9582 aut On Coefficients Problems for Typically Real Functions Related to Gegenbauer Polynomials 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2017 Abstract We solve problems concerning the coefficients of functions in the class %$\mathcal {T}(\lambda )%$ of typically real functions associated with Gegenbauer polynomials. The main aim is to determine the estimates of two expressions: %$|a_4-a_2 a_3|%$ and %$|a_2 a_4 -a_3{}^2|%$. The second one is known as the second Hankel determinant. In order to obtain these bounds, we consider the regions of variability of selected pairs of coefficients for functions in %$\mathcal {T}(\lambda )%$. Furthermore, we find the upper and the lower bounds of functionals of Fekete–Szegö type. Finally, we present some conclusions for the classes %$\mathcal {T}%$ and %$\mathcal {T}(1/2)%$. Gegenbauer polynomials (dpeaa)DE-He213 typically real functions (dpeaa)DE-He213 coefficient problems (dpeaa)DE-He213 Hankel determinants (dpeaa)DE-He213 Figiel, Magdalena aut Futa, Anna aut Enthalten in Mediterranean journal of mathematics Basel : Birkhäuser, 2004 14(2017), 2 vom: 02. März (DE-627)394566831 (DE-600)2160803-9 1660-5454 nnns volume:14 year:2017 number:2 day:02 month:03 https://dx.doi.org/10.1007/s00009-017-0863-4 kostenfrei 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_65 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_267 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 14 2017 2 02 03 |
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10.1007/s00009-017-0863-4 doi (DE-627)SPR000127841 (SPR)s00009-017-0863-4-e DE-627 ger DE-627 rakwb eng Zaprawa, Paweł verfasserin (orcid)0000-0002-7279-9582 aut On Coefficients Problems for Typically Real Functions Related to Gegenbauer Polynomials 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2017 Abstract We solve problems concerning the coefficients of functions in the class %$\mathcal {T}(\lambda )%$ of typically real functions associated with Gegenbauer polynomials. The main aim is to determine the estimates of two expressions: %$|a_4-a_2 a_3|%$ and %$|a_2 a_4 -a_3{}^2|%$. The second one is known as the second Hankel determinant. In order to obtain these bounds, we consider the regions of variability of selected pairs of coefficients for functions in %$\mathcal {T}(\lambda )%$. Furthermore, we find the upper and the lower bounds of functionals of Fekete–Szegö type. Finally, we present some conclusions for the classes %$\mathcal {T}%$ and %$\mathcal {T}(1/2)%$. Gegenbauer polynomials (dpeaa)DE-He213 typically real functions (dpeaa)DE-He213 coefficient problems (dpeaa)DE-He213 Hankel determinants (dpeaa)DE-He213 Figiel, Magdalena aut Futa, Anna aut Enthalten in Mediterranean journal of mathematics Basel : Birkhäuser, 2004 14(2017), 2 vom: 02. März (DE-627)394566831 (DE-600)2160803-9 1660-5454 nnns volume:14 year:2017 number:2 day:02 month:03 https://dx.doi.org/10.1007/s00009-017-0863-4 kostenfrei 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_65 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_267 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 14 2017 2 02 03 |
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10.1007/s00009-017-0863-4 doi (DE-627)SPR000127841 (SPR)s00009-017-0863-4-e DE-627 ger DE-627 rakwb eng Zaprawa, Paweł verfasserin (orcid)0000-0002-7279-9582 aut On Coefficients Problems for Typically Real Functions Related to Gegenbauer Polynomials 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2017 Abstract We solve problems concerning the coefficients of functions in the class %$\mathcal {T}(\lambda )%$ of typically real functions associated with Gegenbauer polynomials. The main aim is to determine the estimates of two expressions: %$|a_4-a_2 a_3|%$ and %$|a_2 a_4 -a_3{}^2|%$. The second one is known as the second Hankel determinant. In order to obtain these bounds, we consider the regions of variability of selected pairs of coefficients for functions in %$\mathcal {T}(\lambda )%$. Furthermore, we find the upper and the lower bounds of functionals of Fekete–Szegö type. Finally, we present some conclusions for the classes %$\mathcal {T}%$ and %$\mathcal {T}(1/2)%$. Gegenbauer polynomials (dpeaa)DE-He213 typically real functions (dpeaa)DE-He213 coefficient problems (dpeaa)DE-He213 Hankel determinants (dpeaa)DE-He213 Figiel, Magdalena aut Futa, Anna aut Enthalten in Mediterranean journal of mathematics Basel : Birkhäuser, 2004 14(2017), 2 vom: 02. März (DE-627)394566831 (DE-600)2160803-9 1660-5454 nnns volume:14 year:2017 number:2 day:02 month:03 https://dx.doi.org/10.1007/s00009-017-0863-4 kostenfrei 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_65 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_267 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 14 2017 2 02 03 |
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10.1007/s00009-017-0863-4 doi (DE-627)SPR000127841 (SPR)s00009-017-0863-4-e DE-627 ger DE-627 rakwb eng Zaprawa, Paweł verfasserin (orcid)0000-0002-7279-9582 aut On Coefficients Problems for Typically Real Functions Related to Gegenbauer Polynomials 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2017 Abstract We solve problems concerning the coefficients of functions in the class %$\mathcal {T}(\lambda )%$ of typically real functions associated with Gegenbauer polynomials. The main aim is to determine the estimates of two expressions: %$|a_4-a_2 a_3|%$ and %$|a_2 a_4 -a_3{}^2|%$. The second one is known as the second Hankel determinant. In order to obtain these bounds, we consider the regions of variability of selected pairs of coefficients for functions in %$\mathcal {T}(\lambda )%$. Furthermore, we find the upper and the lower bounds of functionals of Fekete–Szegö type. Finally, we present some conclusions for the classes %$\mathcal {T}%$ and %$\mathcal {T}(1/2)%$. Gegenbauer polynomials (dpeaa)DE-He213 typically real functions (dpeaa)DE-He213 coefficient problems (dpeaa)DE-He213 Hankel determinants (dpeaa)DE-He213 Figiel, Magdalena aut Futa, Anna aut Enthalten in Mediterranean journal of mathematics Basel : Birkhäuser, 2004 14(2017), 2 vom: 02. März (DE-627)394566831 (DE-600)2160803-9 1660-5454 nnns volume:14 year:2017 number:2 day:02 month:03 https://dx.doi.org/10.1007/s00009-017-0863-4 kostenfrei 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_65 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_267 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 14 2017 2 02 03 |
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Zaprawa, Paweł @@aut@@ Figiel, Magdalena @@aut@@ Futa, Anna @@aut@@ |
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Zaprawa, Paweł |
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Zaprawa, Paweł misc Gegenbauer polynomials misc typically real functions misc coefficient problems misc Hankel determinants On Coefficients Problems for Typically Real Functions Related to Gegenbauer Polynomials |
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On Coefficients Problems for Typically Real Functions Related to Gegenbauer Polynomials Gegenbauer polynomials (dpeaa)DE-He213 typically real functions (dpeaa)DE-He213 coefficient problems (dpeaa)DE-He213 Hankel determinants (dpeaa)DE-He213 |
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misc Gegenbauer polynomials misc typically real functions misc coefficient problems misc Hankel determinants |
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misc Gegenbauer polynomials misc typically real functions misc coefficient problems misc Hankel determinants |
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Elektronische Aufsätze Aufsätze Elektronische Ressource |
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On Coefficients Problems for Typically Real Functions Related to Gegenbauer Polynomials |
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On Coefficients Problems for Typically Real Functions Related to Gegenbauer Polynomials |
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Zaprawa, Paweł |
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Zaprawa, Paweł Figiel, Magdalena Futa, Anna |
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Zaprawa, Paweł |
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on coefficients problems for typically real functions related to gegenbauer polynomials |
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On Coefficients Problems for Typically Real Functions Related to Gegenbauer Polynomials |
| abstract |
Abstract We solve problems concerning the coefficients of functions in the class %$\mathcal {T}(\lambda )%$ of typically real functions associated with Gegenbauer polynomials. The main aim is to determine the estimates of two expressions: %$|a_4-a_2 a_3|%$ and %$|a_2 a_4 -a_3{}^2|%$. The second one is known as the second Hankel determinant. In order to obtain these bounds, we consider the regions of variability of selected pairs of coefficients for functions in %$\mathcal {T}(\lambda )%$. Furthermore, we find the upper and the lower bounds of functionals of Fekete–Szegö type. Finally, we present some conclusions for the classes %$\mathcal {T}%$ and %$\mathcal {T}(1/2)%$. © The Author(s) 2017 |
| abstractGer |
Abstract We solve problems concerning the coefficients of functions in the class %$\mathcal {T}(\lambda )%$ of typically real functions associated with Gegenbauer polynomials. The main aim is to determine the estimates of two expressions: %$|a_4-a_2 a_3|%$ and %$|a_2 a_4 -a_3{}^2|%$. The second one is known as the second Hankel determinant. In order to obtain these bounds, we consider the regions of variability of selected pairs of coefficients for functions in %$\mathcal {T}(\lambda )%$. Furthermore, we find the upper and the lower bounds of functionals of Fekete–Szegö type. Finally, we present some conclusions for the classes %$\mathcal {T}%$ and %$\mathcal {T}(1/2)%$. © The Author(s) 2017 |
| abstract_unstemmed |
Abstract We solve problems concerning the coefficients of functions in the class %$\mathcal {T}(\lambda )%$ of typically real functions associated with Gegenbauer polynomials. The main aim is to determine the estimates of two expressions: %$|a_4-a_2 a_3|%$ and %$|a_2 a_4 -a_3{}^2|%$. The second one is known as the second Hankel determinant. In order to obtain these bounds, we consider the regions of variability of selected pairs of coefficients for functions in %$\mathcal {T}(\lambda )%$. Furthermore, we find the upper and the lower bounds of functionals of Fekete–Szegö type. Finally, we present some conclusions for the classes %$\mathcal {T}%$ and %$\mathcal {T}(1/2)%$. © The Author(s) 2017 |
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| title_short |
On Coefficients Problems for Typically Real Functions Related to Gegenbauer Polynomials |
| url |
https://dx.doi.org/10.1007/s00009-017-0863-4 |
| remote_bool |
true |
| author2 |
Figiel, Magdalena Futa, Anna |
| author2Str |
Figiel, Magdalena Futa, Anna |
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394566831 |
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c |
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true |
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false |
| doi_str |
10.1007/s00009-017-0863-4 |
| up_date |
2024-07-03T14:07:26.201Z |
| _version_ |
1803567126232956928 |
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The main aim is to determine the estimates of two expressions: %$|a_4-a_2 a_3|%$ and %$|a_2 a_4 -a_3{}^2|%$. The second one is known as the second Hankel determinant. In order to obtain these bounds, we consider the regions of variability of selected pairs of coefficients for functions in %$\mathcal {T}(\lambda )%$. Furthermore, we find the upper and the lower bounds of functionals of Fekete–Szegö type. 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