Formulas of special polynomials involving Bernoulli polynomials derived from matrix equations and Laplace transform
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909223008337920 |
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| author | Polat, Ezgi Simsek, Yilmaz |
| author_facet | Polat, Ezgi Simsek, Yilmaz |
| contents | The main purpose and motivation of this article is to create a linear transformation on the polynomial ring of rational numbers. A matrix representation of this linear transformation based on standard fundamentals will be given. For some special cases of this matrix, matrix equations including inverse matrices, the Bell polynomials will be given. With the help of these equations, new formulas containing different polynomials, especially the Bernoulli polynomials, will be given. Finally, by applying the Laplace transform to the generating function for the Bernoulli polynomials, we derive some novel formulas involving the Hurwitz zeta function and infinite series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08503 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Formulas of special polynomials involving Bernoulli polynomials derived from matrix equations and Laplace transform Polat, Ezgi Simsek, Yilmaz General Mathematics 05A15, 11B68, 44A10, 47L05 The main purpose and motivation of this article is to create a linear transformation on the polynomial ring of rational numbers. A matrix representation of this linear transformation based on standard fundamentals will be given. For some special cases of this matrix, matrix equations including inverse matrices, the Bell polynomials will be given. With the help of these equations, new formulas containing different polynomials, especially the Bernoulli polynomials, will be given. Finally, by applying the Laplace transform to the generating function for the Bernoulli polynomials, we derive some novel formulas involving the Hurwitz zeta function and infinite series. |
| title | Formulas of special polynomials involving Bernoulli polynomials derived from matrix equations and Laplace transform |
| topic | General Mathematics 05A15, 11B68, 44A10, 47L05 |
| url | https://arxiv.org/abs/2406.08503 |