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 ...

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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 ...

We solve polynomials algebraically in order to determine the roots - where a curve cuts the \(x\)-axis. A root of a polynomial function, \(f(x)\), is a value for \(x\) for which \(f(x) = 0\).

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 ...

When you buy through links on our articles, Future and its syndication partners may earn a commission. Mathematicians have solved a longstanding algebra problem, providing a general solution for ...

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

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 ...

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 ...