Hermite-based B-spline with their generating functions and moment formulas
Montes Taurus Journal of Pure and Applied Mathematics, cilt.7, sa.3, ss.33-46, 2025 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 7 Sayı: 3
- Basım Tarihi: 2025
- Dergi Adı: Montes Taurus Journal of Pure and Applied Mathematics
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.33-46
- Anahtar Kelimeler: B-spline, Bernoulli numbers, generalized spline moments, generating functions, Hermite polynomials
- Akdeniz Üniversitesi Adresli: Evet
Özet
In this study, generalized spline moments are investigated through generating functions associated with B-splines and certain families of special polynomials. Motivated by the structural role of B-splines in approximation theory and numerical analysis, we construct Hermite-based modifications of spline generating functions. These constructions extend the B-spline through exponential functions involving parameters, thereby enabling new connections with Hermite polynomials. This approach produces new families of spline-type functions that have structural properties from both B-splines and the combinatorial numbers. The resulting identities lead to recursive structures and moment expansions that highlight the interplay between spline theory and combinatorial mathematics. These results reveal a deeper arithmetic perspective on spline functions, connecting them in a meaningful way. A special case is placed on the role of generalized spline moments defined by exponential functions and orthogonal polynomials (Laguerre type), which yield a wide range of applications. The results derived in this work provide insight into the structural behavior of spline functions and indicate possible applications in numerical algorithms, approximation, and analytic number theory.