A new class of generalized Apostol–type Frobenius–Euler polynomials
The paper presents a new type of generalized Apostol-type Frobenius–Euler polynomials and numbers with specific order $ \kappa $ and level $ m $. We establish fundamental identities and properties using generating function techniques, such as summation formulas, differential and integral relations,...
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| Format: | Article |
| Language: | English |
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AIMS Press
2025-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025167 |
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| author | Letelier Castilla William Ramírez Clemente Cesarano Shahid Ahmad Wani Maria-Fernanda Heredia-Moyano |
| author_facet | Letelier Castilla William Ramírez Clemente Cesarano Shahid Ahmad Wani Maria-Fernanda Heredia-Moyano |
| author_sort | Letelier Castilla |
| collection | DOAJ |
| description | The paper presents a new type of generalized Apostol-type Frobenius–Euler polynomials and numbers with specific order $ \kappa $ and level $ m $. We establish fundamental identities and properties using generating function techniques, such as summation formulas, differential and integral relations, and addition theorems. Additionally, we explore the connections between these polynomials and the Stirling numbers of the second kind, as well as other polynomial families. Lastly, we derive a differential equation and a recurrence relation for these new classes of polynomials. Finally, we show applications that can be obtained using these polynomials where the graphs of the zero functions and the meshes are displayed. |
| format | Article |
| id | doaj-art-bf41fd715bed4c1480fd1caebd35c080 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-bf41fd715bed4c1480fd1caebd35c0802025-08-20T01:54:41ZengAIMS PressAIMS Mathematics2473-69882025-02-011023623364110.3934/math.2025167A new class of generalized Apostol–type Frobenius–Euler polynomialsLetelier Castilla0William Ramírez1Clemente Cesarano2Shahid Ahmad Wani3Maria-Fernanda Heredia-Moyano4I.E.E. Normal Superior Nuestra Señora de Fátima. Sabanagrande, ColombiaDepartment of Natural and Exact Sciences, Universidad de la Costa, Calle 58, 55-66, 080002 Barranquilla, ColombiaSection of Mathematics International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, ItalySymbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed) University, Pune, IndiaSection of Mathematics International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, ItalyThe paper presents a new type of generalized Apostol-type Frobenius–Euler polynomials and numbers with specific order $ \kappa $ and level $ m $. We establish fundamental identities and properties using generating function techniques, such as summation formulas, differential and integral relations, and addition theorems. Additionally, we explore the connections between these polynomials and the Stirling numbers of the second kind, as well as other polynomial families. Lastly, we derive a differential equation and a recurrence relation for these new classes of polynomials. Finally, we show applications that can be obtained using these polynomials where the graphs of the zero functions and the meshes are displayed.https://www.aimspress.com/article/doi/10.3934/math.2025167the generalized apostol frobenius–euler polynomialsthe generalized apostol–euler polynomialsdifferential equationsrecurrence relations |
| spellingShingle | Letelier Castilla William Ramírez Clemente Cesarano Shahid Ahmad Wani Maria-Fernanda Heredia-Moyano A new class of generalized Apostol–type Frobenius–Euler polynomials AIMS Mathematics the generalized apostol frobenius–euler polynomials the generalized apostol–euler polynomials differential equations recurrence relations |
| title | A new class of generalized Apostol–type Frobenius–Euler polynomials |
| title_full | A new class of generalized Apostol–type Frobenius–Euler polynomials |
| title_fullStr | A new class of generalized Apostol–type Frobenius–Euler polynomials |
| title_full_unstemmed | A new class of generalized Apostol–type Frobenius–Euler polynomials |
| title_short | A new class of generalized Apostol–type Frobenius–Euler polynomials |
| title_sort | new class of generalized apostol type frobenius euler polynomials |
| topic | the generalized apostol frobenius–euler polynomials the generalized apostol–euler polynomials differential equations recurrence relations |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025167 |
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