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1. CMB 2011 (vol 55 pp. 60)
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Extension of Some Theorems of W. Schwarz 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 Categories:11B37, 11J81 |