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In this paper, we introduce a way to approximate meromorphic functions belonging to Poincaré's ‘new’ class by rational functions. The class consists of meromorphic functions having a ‘théorèm de multiplication’ with a suitable condition, which is a system of difference equations on the transform sendingto, where. Since graphing rational functions is somewhat easy, we are able to know rough graphs of those ‘new’ functions by our result. Our method uses repeated substitutions of the difference equations. [ABSTRACT FROM AUTHOR]

In this paper we will study the irreducibility of q- , q-Painlevé equation of type , in the sense of order using the notion of decomposable extensions. q- is one of the special non-linear q-difference equations of order 2 with symmetry and is also called q- . [ABSTRACT FROM AUTHOR]