On the Rational Recursive Sequence xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i)

The main objective of this paper is to study the boundedness character, the periodic character, the convergence, and the global stability of the positive solutions of the difference equation xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i), n=0,1,2,…, where A, B, αi, βi and the initial conditions x−k,...,x−1,x0 are arbitrary positive real numbers, while k is a positive integer number