Polynomial equations have long served as a cornerstone of mathematical analysis, offering a framework to understand functions, curves, and dynamic systems. In recent years, the study of these ...

A sequence is defined by the recurrence relation \({U_n} = m{U_{n - 1}} + c\) Find the values of \(m\) and \(c\) if \({U_1} = - 3\), \({U_2} = 7\) and \({U_3} = 10 ...

The general terms of third order recursive sequences are expressed in terms of iterative formulas which do not depend on the explicit solution of the auxiliary equations. Some identities associated ...

We consider two semiclassical extensions of the Laguerre weight and their associated sets of orthogonal polynomials. These polynomials satisfy a three-term recurrence relation. We show that the ...