Summary.
We consider meromorphic solutions of functional equations of the form¶¶\( f(cz) = R(z,f(z)) = {\sum_{j=0}^pa_j(z)f(z)^j \over \sum_{j=0}^q b_j(z)f(z)^j} \),¶where the coefficients a j (z),b j (z) are meromorphic functions and c is a complex constant. In fact, for \( |c| > 1 \), any local meromorphic solution around the origin has a meromorphic continuation over \( {\Bbb C} \). We prove a number of results on the growth and value distribution of solutions. In the special case of¶¶\( f(cz) = A(z) + \gamma f(z) + \delta f(z)^2 \),¶where \( c, \gamma, \delta \in {\Bbb C} \), \( |c|>1 \), \( \delta \neq 0 \), and A(z) is entire, we offer a detailed analysis on the number of distinct meromorphic solutions.
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Received: March 16, 2000, revised version: August 26, 2000.
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Gundersen, G., Heittokangas, J., Laine, I. et al. Meromorphic solutions of generalized Schröder equations. Aequat. Math. 63, 110–135 (2002). https://doi.org/10.1007/s00010-002-8010-z
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DOI: https://doi.org/10.1007/s00010-002-8010-z