Abstract
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 sending to , 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.
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