Approximation of Poincaré's new functions by rational functions.

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]