Differentiation formulas for Nörlund sum and applications to Bernoulli polynomials-I
The 24th International Conference of Numerical Analysis and Applied Mathematics, Heraklion, Greece, 15 - 21 September 2026, pp.93-95, (Full Text)
- Publication Type: Conference Paper / Full Text
- City: Heraklion
- Country: Greece
- Page Numbers: pp.93-95
- Akdeniz University Affiliated: Yes
Abstract
In this study, we establish new differential formulas associated with the Nörlund sum by exploiting its differentiation property together with binomial expansions. Based on these formulas, we derive several new identities involving Bernoulli polynomials and provide explicit representations in terms of the Nörlund sum. The obtained results yield new relationships between the Nörlund sum and Bernoulli polynomials and present alternative expressions for these polynomials through differential formulas. Furthermore, the obtained results demonstrate that the Nörlund sum provides an effective framework for deriving identities involving special polynomials.