Document Type
Article
Publication Date
2018
College/Unit
Eberly College of Arts and Sciences
Department/Program/Center
Mathematics
Abstract
A rational function of the form x α1 1 x α2 2 ⋯x αn n x β1 1 +x β2 2 +⋯+x βn n is a Genocchi-Peano example, GPE, provided it is discontinuous, but its restriction to any hyperplane is continuous. We show that the minimal degree D(n) of a GPE of n-variables equals 2 ⌊ e 2 e2−1 n⌋ + 2i for some i ∈ {0, 1, 2}. We also investigate the minimal degree Db(n) of a bounded GPE of n-variables and note that D(n) ≤ Db(n) ≤ n(n + 1). Finding better bounds for numbers Db(n) remains an open problem.
Digital Commons Citation
Ciesielski, Krzysztof, "Minimal Degrees of Genocchi-Peano Functions: Calculus Motivated Number Theoretical Estimates" (2018). Faculty & Staff Scholarship. 853.
https://researchrepository.wvu.edu/faculty_publications/853