2024/05/31 by Ezgi Polat, Polat, Ezgi, Yılmaz Şimşek +1
Mathematics · Physics and Astronomy · #05A15 #11B68 #44A10 #47L05 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #General Mathematics (math.GM) #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.2406.08503
openalex publication_date 2024/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.