New generating functions and formulas for Bernstein-Stancu basis functions and their applications
Montes Taurus Journal of Pure and Applied Mathematics, vol.7, no.3, pp.1-11, 2025 (Scopus)
- Publication Type: Article / Article
- Volume: 7 Issue: 3
- Publication Date: 2025
- Journal Name: Montes Taurus Journal of Pure and Applied Mathematics
- Journal Indexes: Scopus
- Page Numbers: pp.1-11
- Keywords: Bernoulli numbers and polynomials, curves, factorials, gamma and beta functions, Generating functions, recurrences, special sequences and polynomials
- Akdeniz University Affiliated: Yes
Abstract
One of the main aims of this article is to construct new generating functions for the Bernstein-Stancu basis functions, with the help of hypergeometric series, the descending factorial polynomials, and the ascending factorial polynomials. Another main aims is to reveal novel definitions and formulas of the Bernstein-Stancu basis functions with the help of the Euler gamma function and Beta functions. Furthermore, by blending the higher order Bernoulli polynomials, the Lah numbers and the Stirling numbers represented by the descending factorial polynomials, and the ascending factorial polynomials, we derive many new identities and relations of the Bernstein-Stancu basis functions. Finally, recurrence relations, derivative formulas for the Bernstein-Stancu basis functions are also given. Finally, we give Bèzier-type curves in terms of control points and the generalized Bernstein-Stancu basis functions.