On the difference equation xn = xn-2/(bn + cnxn-1xn-2)

Abstract

We prove that the difference equationxn=xn-2/b n+cnxn-1xn-2,n∈ N 0,where (bn)n∈ N0 and (c n)n∈N0 are sequences periodic with period two and the initial values x-2, x-1 are real numbers, can be solved explicitly. Some applications of obtained formulae are given.