Summations of polylogarithms via evaluation transform

In this work, the Evaluation transform is adapted to interpret the polylogarithms as being the Evaluation of the words yxn, for meromorphic kernels and meromorphic inputs. The functional equations on polylogarithms can be obtained, then, via combinatorics on words and the relations between the inputs. Some identities concerning these special functions are also proposed via the products of generating series.

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