Approximations of Apostol-Tangent Polynomials of Complex Order with Parameters a, b, and c
This paper presents new approximation formulas for the tangent polynomials and Apostol-tangent polynomials of complex order, specifically for large values of n. These polynomials are parameterized by a,b, and c. The derivation of these formulas is accomplished through contour integration techniques,...
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| Format: | Article |
| Language: | English |
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Center for Policy, Research and Development Studies
2024-12-01
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| Series: | Recoletos Multidisciplinary Research Journal |
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| Online Access: | https://rmrj.usjr.edu.ph/rmrj/index.php/RMRJ/article/view/2438 |
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| author | Cristina B. Corcino Baby Ann A. Damgo Roberto B. Corcino Joy Ann A. Cañete |
| author_facet | Cristina B. Corcino Baby Ann A. Damgo Roberto B. Corcino Joy Ann A. Cañete |
| author_sort | Cristina B. Corcino |
| collection | DOAJ |
| description | This paper presents new approximation formulas for the tangent polynomials and Apostol-tangent polynomials of complex order, specifically for large values of n. These polynomials are parameterized by a,b, and c. The derivation of these formulas is accomplished through contour integration techniques, where the contour is carefully selected to avoid branch cuts introduced by the presence of multiple singularities within the integration path. The analysis includes a detailed computation of the singularities associated with the generating functions used in this process, ensuring the accuracy and rigor of the derived formulas. Additionally, the paper provides corollary results that reinforce and affirm the newly established formulas, offering a comprehensive understanding of the behavior of these polynomials under specified conditions. |
| format | Article |
| id | doaj-art-cea483b003344c1f97d5b08e1bb66477 |
| institution | Kabale University |
| issn | 2423-1398 2408-3755 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Center for Policy, Research and Development Studies |
| record_format | Article |
| series | Recoletos Multidisciplinary Research Journal |
| spelling | doaj-art-cea483b003344c1f97d5b08e1bb664772025-01-07T08:29:01ZengCenter for Policy, Research and Development StudiesRecoletos Multidisciplinary Research Journal2423-13982408-37552024-12-01122779010.32871/rmrj2412.02.06Approximations of Apostol-Tangent Polynomials of Complex Order with Parameters a, b, and cCristina B. Corcino0https://orcid.org/0000-0003-1634-9605Baby Ann A. Damgo1https://orcid.org/0009-0007-1776-7493Roberto B. Corcino2https://orcid.org/0000-0003-1681-1804Joy Ann A. Cañete3https://orcid.org/0009-0001-9078-3074(1) Research Institute for Computational Mathematics and Physics, Cebu Normal University, Cebu City, Philippines; (2) Mathematics Department, Cebu Normal University, Cebu City, PhilippinesDepartment of Mathematics and Statistics, Cebu Technological University, Cebu City, Philippines(1) Research Institute for Computational Mathematics and Physics, Cebu Normal University, Cebu City, Philippines; (2) Mathematics Department, Cebu Normal University, Cebu City, PhilippinesDepartment of Mathematics, Visayas State University, Baybay City, PhilippinesThis paper presents new approximation formulas for the tangent polynomials and Apostol-tangent polynomials of complex order, specifically for large values of n. These polynomials are parameterized by a,b, and c. The derivation of these formulas is accomplished through contour integration techniques, where the contour is carefully selected to avoid branch cuts introduced by the presence of multiple singularities within the integration path. The analysis includes a detailed computation of the singularities associated with the generating functions used in this process, ensuring the accuracy and rigor of the derived formulas. Additionally, the paper provides corollary results that reinforce and affirm the newly established formulas, offering a comprehensive understanding of the behavior of these polynomials under specified conditions.https://rmrj.usjr.edu.ph/rmrj/index.php/RMRJ/article/view/2438asymptotic approximationtangent polynomialsapostol-tangent polynomials |
| spellingShingle | Cristina B. Corcino Baby Ann A. Damgo Roberto B. Corcino Joy Ann A. Cañete Approximations of Apostol-Tangent Polynomials of Complex Order with Parameters a, b, and c Recoletos Multidisciplinary Research Journal asymptotic approximation tangent polynomials apostol-tangent polynomials |
| title | Approximations of Apostol-Tangent Polynomials of Complex Order with Parameters a, b, and c |
| title_full | Approximations of Apostol-Tangent Polynomials of Complex Order with Parameters a, b, and c |
| title_fullStr | Approximations of Apostol-Tangent Polynomials of Complex Order with Parameters a, b, and c |
| title_full_unstemmed | Approximations of Apostol-Tangent Polynomials of Complex Order with Parameters a, b, and c |
| title_short | Approximations of Apostol-Tangent Polynomials of Complex Order with Parameters a, b, and c |
| title_sort | approximations of apostol tangent polynomials of complex order with parameters a b and c |
| topic | asymptotic approximation tangent polynomials apostol-tangent polynomials |
| url | https://rmrj.usjr.edu.ph/rmrj/index.php/RMRJ/article/view/2438 |
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