Polynomial equations are fundamental concepts in mathematics that define relationships between numbers and variables in a structured manner. In mathematics, various equations are composed using ...

The theory of Appell polynomials has long intrigued researchers due to its elegant algebraic structure and rich connections with differential equations. At its core, an Appell sequence is ...

The intertwined study of orthogonal polynomials and Painlevé equations continues to be a fertile area of research at the confluence of mathematical analysis and theoretical physics. Orthogonal ...

Polynomial equations are a cornerstone of modern science, providing a mathematical basis for celestial mechanics, computer graphics, market growth predictions and much more. But although most high ...

Three researchers from Bristol University are seeking to develop methods for analysing the distribution of integer solutions to polynomial equations. How do you know when a polynomial equation has ...

In 1922 Ritt described polynomial solutions of the functional equation P(f) = Q(g). In this paper we describe solutions of the equation above in the case when P, Q are polynomials while f, g are ...

Equations, like numbers, cannot always be split into simpler elements. Researchers have now proved that such “prime” equations become ubiquitous as equations grow larger. Prime numbers get all the ...

By combining the language of groups with that of geometry and linear algebra, Marius Sophus Lie created one of math’s most ...

A mathematician has uncovered a way of answering some of algebra's oldest problems. University of New South Wales Honorary Professor Norman Wildberger, has revealed a potentially game-changing ...