On new generalized discrete \(U\)-Bernoulli-Korobov-kind polynomials and some of their properties
Authors
A. Urieles
- Programa de Matematicas, Universidad del Atlantico, Km 7 Via Pto. Colombia, Barranquilla, Colombia.
J. L. Escalante
- Programa de Matematicas, Universidad del Atlantico, Km 7 Via Pto. Colombia, Barranquilla, Colombia.
M. J. Ortega
- Departamento de Ciencias Naturales y Exactas, Universidad de la Costa, Barranquilla, Colombia.
Abstract
The object of this study is to introduce the new generalized discrete U-Bernoulli-Korobov-kind polynomials. Additionally, we give several of its explicit representations, as well as relations with other families of polynomials. We state some properties for the \(\Delta\) and \(\nabla\) operators associated with this polynomial class. Finally, we focus our attention on the orthogonality relation and the three-term recurrence formula satisfied by these polynomials.
Share and Cite
ISRP Style
A. Urieles, J. L. Escalante, M. J. Ortega, On new generalized discrete \(U\)-Bernoulli-Korobov-kind polynomials and some of their properties, Journal of Mathematics and Computer Science, 36 (2025), no. 1, 52--69
AMA Style
Urieles A., Escalante J. L., Ortega M. J., On new generalized discrete \(U\)-Bernoulli-Korobov-kind polynomials and some of their properties. J Math Comput SCI-JM. (2025); 36(1):52--69
Chicago/Turabian Style
Urieles, A., Escalante, J. L., Ortega, M. J.. "On new generalized discrete \(U\)-Bernoulli-Korobov-kind polynomials and some of their properties." Journal of Mathematics and Computer Science, 36, no. 1 (2025): 52--69
Keywords
- Orthogonal polynomials
- recurrence relations
- Bernoulli polynomials
- Bernoulli polynomials of the second kind
- Cauchy numbers
- the backward and forward difference operators
- Pearson-type difference equation
MSC
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