On the extension of analytic solutions of first-order difference equations

Rod Halburd, Risto Korhonen, Yan Liu +1

We will consider first-order difference equations of the form \[ y(z+1) = \frac{λy(z)+a_2(z)y(z)^2+\cdots+a_p(z)y(z)^p}{1 + b_1(z)y(z)+\cdots+b_q(z)y(z)^q}, \] where $λ\in\mathbb{C…