New $U$-Bernoulli, $U$-Euler and $U$-Genocchi polynomials and their matrices

  • W. Ramírez University of the Coast, Calle 58 # 55 - 66, Barranquilla, Colombia
  • D. Bedoya Metropolitana University, Calle 76 # 42 - 78, Las Mercedes, Barranquilla, Colombia
  • A. Urieles University of Atlántico, Av. 20 De Julio # 50 - 53, Nte. Centro Historico, Barranquilla, Colombia
  • C. Cesarano International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy
  • M. Ortega University of the Coast, Calle 58 # 55 - 66, Barranquilla, Colombia
Keywords: $U$-Bernoulli polynomial, $U$-Euler polynomial, generalized $U$-Bernoulli polynomial, generalized $U$-Euler polynomial, $U$-Bernoulli polynomials matrix, $U$-Euler polynomials matrix, Pascal matrix
Published online: 2023-11-21


In this paper, we introduce the $U$-Bernoulli, $U$-Euler, and $U$-Genocchi polynomials, their numbers, and their relationship with the Riemann zeta function. We also derive the Apostol-type generalizations to obtain some of their algebraic and differential properties. We introduce generalized $U$-Bernoulli, $U$-Euler and $U$-Genocchi polynomial Pascal-type matrix. We deduce some product formulas related to this matrix. Furthermore, we establish some explicit expressions for the $U$-Bernoulli, $U$-Euler, and $U$-Genocchi polynomial matrices, which involves the generalized Pascal matrix.

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How to Cite
Ramírez W., Bedoya D., Urieles A., Cesarano C., Ortega M. New $U$-Bernoulli, $U$-Euler and $U$-Genocchi Polynomials and Their Matrices. Carpathian Math. Publ. 2023, 15 (2), 449-467.