Irreducibility and hypertranscendence of non-linear difference equations

点击翻译按钮获取中文摘要

There are special second-order algebraic difference equations called discrete Painleve equations. The equation called d-Painleve equation of type D7(1) is one of them. Its irreducibility in the sense of decomposable extension was proved. The irreducibility implies that the transcendental function solution cannot be built from rational functions by reiterating algebraic operations and the taking of solutions of linear difference equations or first-order algebraic difference equations. A standard form of difference Riccati equations for any transforming operator was also studied.