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Several theories have been proposed to generalise the concept of analyticcontinuation to holomorphic functions of the disc for which the circle is anatural boundary. Elaborating on Breuer-Simon's work on "right limits" of powerseries, Baladi-Marmi-Sauzin recently introduced the notion of "renascent rightlimit" and "rrl-continuation". We discuss a few examples and considerparticularly the classical example of "Poincar{\'e} simple pole series" in thislight. These functions are represented in the disc as series of infinitely manysimple poles located on the circle; they appear for instance in small divisorproblems in dynamics. We prove that any such function admits a uniquerrl-continuation, which coincides with the function obtained outside the discby summing the simple pole expansion. We also discuss the relation withmonogenic regularity in the sense of Borel.

Generalised continuation by means of right limits