Linearization And Solutions Of The Discrete Painlevé-III Equation
We present particular solutions of the discrete Painlevé III (d-P$\rm_{III}$) equation of rational and special function (Bessel) type. These solutions allow us to establish a close parallel between this discrete equation and its continuous counterpart. Moreover, we propose an alternate form for d-P$\rm_{III}$ and confirm its integrability by explicitly deriving its Lax pair.
solv-int↗