The purpose of this paper is to provide explicit formulas for a variety of probabilistic quantities associated with an asymmetric random walk on a finite rectangular lattice with absorbing barriers.

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 ...

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 ...

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 ...