Evaluating log-tangent integrals via Euler sums
An investigation into the representation of integrals involving the product of the logarithm and the arctan functions, reducing to log-tangent integrals, will be undertaken in this paper. We will show that in many cases these integrals take an explicit form involving the Riemann zeta function, the D...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2022-02-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/13100 |
| _version_ | 1818896775680884736 |
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| author | Anthony Sofo |
| author_facet | Anthony Sofo |
| author_sort | Anthony Sofo |
| collection | DOAJ |
| description | An investigation into the representation of integrals involving the product of the logarithm and the arctan functions, reducing to log-tangent integrals, will be undertaken in this paper. We will show that in many cases these integrals take an explicit form involving the Riemann zeta function, the Dirichlet eta function, Dirichlet lambda function and many other special functions. Some examples illustrating the theorems will be detailed. |
| first_indexed | 2024-12-19T19:05:39Z |
| format | Article |
| id | doaj.art-a79bfd7f287b45399b6e70c00f04e2bf |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-19T19:05:39Z |
| publishDate | 2022-02-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-a79bfd7f287b45399b6e70c00f04e2bf2022-12-21T20:09:28ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102022-02-012711–181–1810.3846/mma.2022.1310013100Evaluating log-tangent integrals via Euler sumsAnthony Sofo0College of Engineering and Science, Victoria University, Ballarat Rd., 8001 Melbourne, AustraliaAn investigation into the representation of integrals involving the product of the logarithm and the arctan functions, reducing to log-tangent integrals, will be undertaken in this paper. We will show that in many cases these integrals take an explicit form involving the Riemann zeta function, the Dirichlet eta function, Dirichlet lambda function and many other special functions. Some examples illustrating the theorems will be detailed.https://journals.vgtu.lt/index.php/MMA/article/view/13100dirichlet beta functionslog-tangent integraleuler sumsdirichlet lambda functionzeta functions |
| spellingShingle | Anthony Sofo Evaluating log-tangent integrals via Euler sums Mathematical Modelling and Analysis dirichlet beta functions log-tangent integral euler sums dirichlet lambda function zeta functions |
| title | Evaluating log-tangent integrals via Euler sums |
| title_full | Evaluating log-tangent integrals via Euler sums |
| title_fullStr | Evaluating log-tangent integrals via Euler sums |
| title_full_unstemmed | Evaluating log-tangent integrals via Euler sums |
| title_short | Evaluating log-tangent integrals via Euler sums |
| title_sort | evaluating log tangent integrals via euler sums |
| topic | dirichlet beta functions log-tangent integral euler sums dirichlet lambda function zeta functions |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/13100 |
| work_keys_str_mv | AT anthonysofo evaluatinglogtangentintegralsviaeulersums |