Polynomials and power functions are the foundation for modelling non-linear relationships. Polynomial functions such as quadratic, cubic and quartic model variables raised to exponents of different ...

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

Chromatic symmetric functions and combinatorial polynomials are central constructs in modern algebraic combinatorics, extending classical graph invariants into rich algebraic frameworks. Originating ...

Mathematics of Computation, Vol. 34, No. 150 (Apr., 1980), pp. 441-463 (23 pages) Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are ...

Abstract: The main focus of this investigation is the applications of Sigmoid functions. Due to its various uses in physics, engineering, and computer science, we introduce Bell-based ...

The polynomial-solutions of the self-adjoint differential equations $D\left[ {\exp \left( { - x_1^{2k}} \right)Dy} \right] + \lambda {x^{2k - 2}}\exp \left( { - {x ...

In the Introduction to the Derivative video we introduce the notion of the derivative of a function and explain how the derivative captures the instantaneous rate of change of a function. In the ...

ABSTRACT: Utilization of the shift operator to represent Euler polynomials as polynomials of Appell type leads directly to its algebraic properties, its relations with powers sums; may be all its ...