where $a_0,\ a_1,\ a_2,\ ...\ a_k, c_0,\ c_1,\ c_2,\ ...\ c_k \in \mathbb{R}$ (although these can be complex numbers $\mathbb{C}$ as well, but for simplicity we keep ...

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 ...

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 ...

Every positive sequence generated by the Fibonacci recurrence relation diverges to infinity. However, every positive sequence generated by the square root of the Fibonacci recurrence relation ...

Department of Mathematics, College of Science, Qassim University, Al-Mulida, Saudi Arabia. The sequences () and () are called the Szego-Jacobi parameters of. The starting point of the quantum ...