NEW FORMULAS FOR BERNOULLI POLYNOMIALS WITH APPLICATIONS OF MATRIX EQUATIONS AND LAPLACE TRANSFORM
Publications de l'Institut Mathematique, vol.116, no.130, pp.59-74, 2024 (ESCI)
- Publication Type: Article / Article
- Volume: 116 Issue: 130
- Publication Date: 2024
- Doi Number: 10.2298/pim2430059p
- Journal Name: Publications de l'Institut Mathematique
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Central & Eastern European Academic Source (CEEAS), MathSciNet, zbMATH
- Page Numbers: pp.59-74
- Keywords: Bernoulli polynomials and numbers, computational algorithm, generating functions, Hurwitz zeta function, inverse matrix, Laplace transform, linear transformation
- Akdeniz University Affiliated: Yes
Abstract
We give a linear transformation on the polynomial ring of rational numbers. A matrix representation of this linear transformation based on standard bases is constructed. For some special cases of this matrix, matrix equations including inverse matrices related to the Bell polynomials and Diophantine equation are obtained. With the help of these equations, new formulas containing different polynomials with the Bernoulli polynomials are found. In order to compute these polynomials, a computational algorithm is 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.