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The unified equation P4,34 is closely related to the well-known Painleve equations P2 and P4. We discuss various properties of solutions of P4,34, including one-parameter families of solutions, Backlund transformations, regular systems for expansions around zeros and poles and value distribution. In particular, we give estimates of defects and multiplicity indices of transcen- dental meromorphic solutions of this equation. Moreover, we study solutions of P4,34 from the perspective of Petrenko's theory, which is also new for P2,P4 and P34. We give estimates of devi- ations and analyse the sets of exceptional values in the sense of Petrenko for equations P2,P4,P34 and the unified equation P4,34.

Meromorphic solutions of P_4,34 and their value distribution