Two Forms for Maclaurin Power Series Expansion of Logarithmic Expression Involving Tangent Function
In view of a general formula for higher order derivatives of the ratio of two differentiable functions, the authors establish the first form for the Maclaurin power series expansion of a logarithmic expression in term of determinants of special Hessenberg matrices whose elements involve the Bernoull...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/9/1686 |
| _version_ | 1797576662300229632 |
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| author | Yue-Wu Li Feng Qi Wei-Shih Du |
| author_facet | Yue-Wu Li Feng Qi Wei-Shih Du |
| author_sort | Yue-Wu Li |
| collection | DOAJ |
| description | In view of a general formula for higher order derivatives of the ratio of two differentiable functions, the authors establish the first form for the Maclaurin power series expansion of a logarithmic expression in term of determinants of special Hessenberg matrices whose elements involve the Bernoulli numbers. On the other hand, for comparison, the authors recite and revise the second form for the Maclaurin power series expansion of the logarithmic expression in terms of the Bessel zeta functions and the Bernoulli numbers. |
| first_indexed | 2024-03-10T21:55:03Z |
| format | Article |
| id | doaj.art-f2cf0207411a495796fae402f5ae5309 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T21:55:03Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-f2cf0207411a495796fae402f5ae53092023-11-19T13:11:13ZengMDPI AGSymmetry2073-89942023-09-01159168610.3390/sym15091686Two Forms for Maclaurin Power Series Expansion of Logarithmic Expression Involving Tangent FunctionYue-Wu Li0Feng Qi1Wei-Shih Du2School of Mathematics and Physics, Hulunbuir University, Inner Mongolia, Hulunbuir 021008, ChinaSchool of Mathematics and Physics, Hulunbuir University, Inner Mongolia, Hulunbuir 021008, ChinaDepartment of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, TaiwanIn view of a general formula for higher order derivatives of the ratio of two differentiable functions, the authors establish the first form for the Maclaurin power series expansion of a logarithmic expression in term of determinants of special Hessenberg matrices whose elements involve the Bernoulli numbers. On the other hand, for comparison, the authors recite and revise the second form for the Maclaurin power series expansion of the logarithmic expression in terms of the Bessel zeta functions and the Bernoulli numbers.https://www.mdpi.com/2073-8994/15/9/1686maclaurin power series expansionhessenberg matrixdeterminantbernoulli numberbessel zeta functionlogarithmic expression |
| spellingShingle | Yue-Wu Li Feng Qi Wei-Shih Du Two Forms for Maclaurin Power Series Expansion of Logarithmic Expression Involving Tangent Function Symmetry maclaurin power series expansion hessenberg matrix determinant bernoulli number bessel zeta function logarithmic expression |
| title | Two Forms for Maclaurin Power Series Expansion of Logarithmic Expression Involving Tangent Function |
| title_full | Two Forms for Maclaurin Power Series Expansion of Logarithmic Expression Involving Tangent Function |
| title_fullStr | Two Forms for Maclaurin Power Series Expansion of Logarithmic Expression Involving Tangent Function |
| title_full_unstemmed | Two Forms for Maclaurin Power Series Expansion of Logarithmic Expression Involving Tangent Function |
| title_short | Two Forms for Maclaurin Power Series Expansion of Logarithmic Expression Involving Tangent Function |
| title_sort | two forms for maclaurin power series expansion of logarithmic expression involving tangent function |
| topic | maclaurin power series expansion hessenberg matrix determinant bernoulli number bessel zeta function logarithmic expression |
| url | https://www.mdpi.com/2073-8994/15/9/1686 |
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