Approximations related to the complete p-elliptic integrals
In this paper, the authors present some monotonicity properties for certain functions involving the complete p-elliptic integrals of the first and second kinds, by showing the monotonicity and concavity-convexity properties of certain combinations defined in terms of Kp{{\mathscr{K}}}_{p}, Ep{{\math...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-09-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2022-0493 |
| _version_ | 1797989307290484736 |
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| author | Zhong Genhong Ma Xiaoyan Wang Fei |
| author_facet | Zhong Genhong Ma Xiaoyan Wang Fei |
| author_sort | Zhong Genhong |
| collection | DOAJ |
| description | In this paper, the authors present some monotonicity properties for certain functions involving the complete p-elliptic integrals of the first and second kinds, by showing the monotonicity and concavity-convexity properties of certain combinations defined in terms of Kp{{\mathscr{K}}}_{p}, Ep{{\mathscr{E}}}_{p} and the inverse hyperbolic tangent arthp{{\rm{arth}}}_{p}, which is of importance in the computation of the generalized pi and in the elementary proof of Ramanujan’s cubic transformation. By these results, several well-known results for the classical complete elliptic integrals including its bounds and logarithmic inequalities are remarkably improved. |
| first_indexed | 2024-04-11T08:18:14Z |
| format | Article |
| id | doaj.art-83c316c205d344e9a099f3743d83cddc |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-04-11T08:18:14Z |
| publishDate | 2022-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-83c316c205d344e9a099f3743d83cddc2022-12-22T04:35:04ZengDe GruyterOpen Mathematics2391-54552022-09-012011046105610.1515/math-2022-0493Approximations related to the complete p-elliptic integralsZhong Genhong0Ma Xiaoyan1Wang Fei2Keyi College of Zhejiang Sci-Tech University, Shaoxing 312300, ChinaDepartment of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, ChinaZhejiang Institute of Mechanical and Electrical Engineering, Hangzhou 310053, ChinaIn this paper, the authors present some monotonicity properties for certain functions involving the complete p-elliptic integrals of the first and second kinds, by showing the monotonicity and concavity-convexity properties of certain combinations defined in terms of Kp{{\mathscr{K}}}_{p}, Ep{{\mathscr{E}}}_{p} and the inverse hyperbolic tangent arthp{{\rm{arth}}}_{p}, which is of importance in the computation of the generalized pi and in the elementary proof of Ramanujan’s cubic transformation. By these results, several well-known results for the classical complete elliptic integrals including its bounds and logarithmic inequalities are remarkably improved.https://doi.org/10.1515/math-2022-0493complete p-elliptic integralsmonotonicityinequalitybounds inequalitieslogarithmic inequalities33c7533e0533f05 |
| spellingShingle | Zhong Genhong Ma Xiaoyan Wang Fei Approximations related to the complete p-elliptic integrals Open Mathematics complete p-elliptic integrals monotonicity inequality bounds inequalities logarithmic inequalities 33c75 33e05 33f05 |
| title | Approximations related to the complete p-elliptic integrals |
| title_full | Approximations related to the complete p-elliptic integrals |
| title_fullStr | Approximations related to the complete p-elliptic integrals |
| title_full_unstemmed | Approximations related to the complete p-elliptic integrals |
| title_short | Approximations related to the complete p-elliptic integrals |
| title_sort | approximations related to the complete p elliptic integrals |
| topic | complete p-elliptic integrals monotonicity inequality bounds inequalities logarithmic inequalities 33c75 33e05 33f05 |
| url | https://doi.org/10.1515/math-2022-0493 |
| work_keys_str_mv | AT zhonggenhong approximationsrelatedtothecompletepellipticintegrals AT maxiaoyan approximationsrelatedtothecompletepellipticintegrals AT wangfei approximationsrelatedtothecompletepellipticintegrals |