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Then (i) λ ( w ) = ρ ( w ) ;   (ii) w has at most one Borel exceptional value for ρ ( w ) > 0.  .

λ ( w ) = ρ ( w ) ; w has at most one Borel exceptional value for ρ ( w ) > 0. Example 1.3 The function w 1 ( z ) = 3 ( e 2 π i z + z ) 2 4 ( e 2 π i z + z + 1 ) ( e 2 π i z + z − 1 ) is a solution of the difference equation w ¯ w ̲ w ( w − 1 ) = − 3 3 4 4.

λ ( w ) = ρ ( w ) ; w has at most one non-zero Borel exceptional value for ρ ( w ) > 0. The purpose of this paper is to study the remaining difference equation (1.2a) with constant coefficients.

λ ( w ) = τ ( w ) = ρ ( w ) ; If λ = 0, then w has at most one non-zero Borel exceptional value for ρ ( w ) > 0. Proof Denote ϕ ( z ) = w ( z ) − z.

where η (≠0), λ ≠ 1 are constants, then (i) λ ( w ) = ρ ( w ) ;   (ii) if λ = 0, then w has at most one non-zero Borel exceptional value for ρ ( w ) > 0.  .