Geodesic
On the functional equation $f(p(z))=g(q(z))$, where~$p$ and~$q$ are ``generalized'' polynomials and~$f$ and~$g$ are meromorphic functions
Izvestiya. Mathematics , Tome 60 (1996) no. 5, pp. 963-984.

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We find all the solutions of the equation $f(p(z))=g(q(z))$, where $p$ and $q$ are polynomials and $p$ and $q$ are transcendental meromorphic functions in $\mathbb C$. In fact, a more general algebraic problem is solved. 
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S. A. Lysenko. On the functional equation $f(p(z))=g(q(z))$, where~$p$ and~$q$ are ``generalized'' polynomials and~$f$ and~$g$ are meromorphic functions. Izvestiya. Mathematics , Tome 60 (1996) no. 5, pp. 963-984. http://geodesic.mathdoc.fr/item/IM2_1996_60_5_a5/

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