Hankel Determinant Containing Logarithmic Coefficients for Bounded Turning Functions Connected to a Three-Leaf-Shaped Domain
The purpose of this study was to obtain the sharp Hankel determinant <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mrow><mn>2</mn><mo>,</mo&g...
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MDPI AG
2022-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/16/2924 |
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| author | Lei Shi Muhammad Arif Mohsan Raza Muhammad Abbas |
| author_facet | Lei Shi Muhammad Arif Mohsan Raza Muhammad Abbas |
| author_sort | Lei Shi |
| collection | DOAJ |
| description | The purpose of this study was to obtain the sharp Hankel determinant <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub><mfenced separators="" open="(" close=")"><msub><mi>F</mi><mi>f</mi></msub><mo>/</mo><mn>2</mn></mfenced></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub><mfenced separators="" open="(" close=")"><msub><mi>F</mi><mi>f</mi></msub><mo>/</mo><mn>2</mn></mfenced></mrow></semantics></math></inline-formula> with a logarithmic coefficient as entry for the class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">BT</mi><mrow><mn>3</mn><mi mathvariant="script">L</mi></mrow></msub></semantics></math></inline-formula> of bounded turning functions connected with a three-leaf-shaped domain. In this study, we developed a novel method to prove the bound sharpness. Although the calculations are much easier using numerical analysis, all the proofs of our results can be checked with a basic knowledge of calculus. |
| first_indexed | 2024-03-09T09:52:46Z |
| format | Article |
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| language | English |
| last_indexed | 2024-03-09T09:52:46Z |
| publishDate | 2022-08-01 |
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| series | Mathematics |
| spelling | doaj.art-4e29a1e5836e42d2866da3c76558ad802023-12-01T23:57:34ZengMDPI AGMathematics2227-73902022-08-011016292410.3390/math10162924Hankel Determinant Containing Logarithmic Coefficients for Bounded Turning Functions Connected to a Three-Leaf-Shaped DomainLei Shi0Muhammad Arif1Mohsan Raza2Muhammad Abbas3School of Mathematics and Statistics, Anyang Normal University, Anyang 455002, ChinaDepartment of Mathematics, Abdul Wali khan University Mardan, Mardan 23200, PakistanDepartment of Mathematics, Government College University, Faisalabad 38000, PakistanDepartment of Mathematics, Abdul Wali khan University Mardan, Mardan 23200, PakistanThe purpose of this study was to obtain the sharp Hankel determinant <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub><mfenced separators="" open="(" close=")"><msub><mi>F</mi><mi>f</mi></msub><mo>/</mo><mn>2</mn></mfenced></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub><mfenced separators="" open="(" close=")"><msub><mi>F</mi><mi>f</mi></msub><mo>/</mo><mn>2</mn></mfenced></mrow></semantics></math></inline-formula> with a logarithmic coefficient as entry for the class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">BT</mi><mrow><mn>3</mn><mi mathvariant="script">L</mi></mrow></msub></semantics></math></inline-formula> of bounded turning functions connected with a three-leaf-shaped domain. In this study, we developed a novel method to prove the bound sharpness. Although the calculations are much easier using numerical analysis, all the proofs of our results can be checked with a basic knowledge of calculus.https://www.mdpi.com/2227-7390/10/16/2924Hankel determinantlogarithmic coefficientbounded turning functionsthree-leaf-shaped domain |
| spellingShingle | Lei Shi Muhammad Arif Mohsan Raza Muhammad Abbas Hankel Determinant Containing Logarithmic Coefficients for Bounded Turning Functions Connected to a Three-Leaf-Shaped Domain Mathematics Hankel determinant logarithmic coefficient bounded turning functions three-leaf-shaped domain |
| title | Hankel Determinant Containing Logarithmic Coefficients for Bounded Turning Functions Connected to a Three-Leaf-Shaped Domain |
| title_full | Hankel Determinant Containing Logarithmic Coefficients for Bounded Turning Functions Connected to a Three-Leaf-Shaped Domain |
| title_fullStr | Hankel Determinant Containing Logarithmic Coefficients for Bounded Turning Functions Connected to a Three-Leaf-Shaped Domain |
| title_full_unstemmed | Hankel Determinant Containing Logarithmic Coefficients for Bounded Turning Functions Connected to a Three-Leaf-Shaped Domain |
| title_short | Hankel Determinant Containing Logarithmic Coefficients for Bounded Turning Functions Connected to a Three-Leaf-Shaped Domain |
| title_sort | hankel determinant containing logarithmic coefficients for bounded turning functions connected to a three leaf shaped domain |
| topic | Hankel determinant logarithmic coefficient bounded turning functions three-leaf-shaped domain |
| url | https://www.mdpi.com/2227-7390/10/16/2924 |
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