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 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 ...

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 ...