NEW FORMULAS FOR BERNOULLI POLYNOMIALS WITH APPLICATIONS OF MATRIX EQUATIONS AND LAPLACE TRANSFORM

Polat E., ŞİMŞEK Y.

Publications de l'Institut Mathematique, cilt.116, sa.130, ss.59-74, 2024 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 116 Sayı: 130
  • Basım Tarihi: 2024
  • Doi Numarası: 10.2298/pim2430059p
  • Dergi Adı: Publications de l'Institut Mathematique
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Central & Eastern European Academic Source (CEEAS), MathSciNet, zbMATH
  • Sayfa Sayıları: ss.59-74
  • Anahtar Kelimeler: Bernoulli polynomials and numbers, computational algorithm, generating functions, Hurwitz zeta function, inverse matrix, Laplace transform, linear transformation
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.