Weierstrass as a reader of Poincaré׳s early works

•Gap series.•Analytic functions with natural boundaries.•Uniformisation theorem.•The Volterra–Poincaré theorem.•n-Body problem.

From the very beginning of his scientific career Poincaré found an attentive reader in Weierstrass. To support this claim, in the apparent lack of direct relationship between them, in the present paper I take into account indirect sources such as Mittag-Leffler׳s letters to Poincaré and Weierstrass, and Weierstrass׳s letters to S. Kovalevskaya and H. A. Schwarz. These letters provide evidence of Weierstrass׳s interest in the achievements of the young French mathematician, including in particular his early statement of the uniformisation theorem. In addition, such subjects as gap series, the Poincaré–Volterra theorem and the n-body problem are also discussed.