10/08/2008, 04:22 PM

We know that the recurrence for

(1)

(2)

has as the only entire solution that is bounded on the strip .

The image of under is an annulus for and so bounded. We know that for complex the function is not bounded on (the image is kinda infinite spiral) for any . The question remains whether

Conjecture

There is no entire solution that satisfies (1) and (2) and is bounded on for complex .

(1)

(2)

has as the only entire solution that is bounded on the strip .

The image of under is an annulus for and so bounded. We know that for complex the function is not bounded on (the image is kinda infinite spiral) for any . The question remains whether

Conjecture

There is no entire solution that satisfies (1) and (2) and is bounded on for complex .