Transcendental solution to linear coefficient non-homogeneous second order recurrence relation with constant non-homogenity
Published:
This paper captures the behavior of a second order recurrence relation with linear coefficients and a constant non-homogenity. By varying the second initial value we find a unique explicit solution which is bounded and converges even to $0$ while all solutions for different second initial values diverge to $\pm\infty$. Observations on the structure of this solution and implications for computational approaches are discussed.