Polynomial and special function theory remains a vibrant area of mathematical research, interweaving classical algebra with advanced analysis. At its core, the study concerns algebraic expressions ...

Bernstein polynomial estimation provides a robust nonparametric technique for approximating both density and distribution functions. Based on the properties of Bernstein polynomials, which uniformly ...

Polynomial functions containing terms with non-integer powers are studied to disclose possible approaches for obtaining their roots as well as employing them for curve-fitting purposes. Several ...

The original code is as old as from 1995 and was written by Gerhard Krucker (see http://www.krucker.ch/skripten-uebungen/IAMSkript/IAMKap3.pdf#page=14). So all ...

Starting with the binomial coefficient and using its infinite product representation, the infinite product representation of the gamma function and of the zeta function are composed of an exponential ...

Abstract: We propose using (bilinear) sum-of-squares programming for obtaining inner bounds of RoAs for dynamical systems with polynomial vector fields. We search for polynomial as well as composite ...

Abstract: In this article, we search for polynomial Lyapunov functions beyond the quadratic form to investigate the synchronization problems of nonlinearly coupled complex networks. First, with a ...