In this paper, we prove that a non--zero power series $F(z)\in\mathbb{C} [\mkern-3mu[ z]\mkern-3mu] $ satisfying $$F(z^d)=F(z)+\frac{A(z)}{B(z)},$$ where $d\geq 2$, $A(z),B(z)\in\mathbb{C}[z]$ with $A(z)\neq 0$ and $\deg A(z),\deg B(z)

Keywords:

functional equations, transcendence, power series functional equations, transcendence, power series

MSC Classifications:

11B37, 11J81 show english descriptions Recurrences {For applications to special functions, see 33-XX}
Transcendence (general theory) 11B37 - Recurrences {For applications to special functions, see 33-XX}
11J81 - Transcendence (general theory)

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