Some properties of algebraic difference equations of first order
Abstract We prove that if g ( z ) $g(z)$ is a finite-order transcendental meromorphic solution of ( △ c g ( z ) ) 2 = A ( z ) g ( z ) g ( z + c ) + B ( z ) , $$\bigl(\triangle_{c} g(z)\bigr)^{2}=A(z)g(z)g(z+c)+B(z), $$ where A ( z ) $A(z)$ and B ( z ) $B(z)$ are polynomials such that deg A ( z ) >...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-10-01
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| Series: | Advances in Difference Equations |
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| Online Access: | http://link.springer.com/article/10.1186/s13662-017-1395-8 |
| Summary: | Abstract We prove that if g ( z ) $g(z)$ is a finite-order transcendental meromorphic solution of ( △ c g ( z ) ) 2 = A ( z ) g ( z ) g ( z + c ) + B ( z ) , $$\bigl(\triangle_{c} g(z)\bigr)^{2}=A(z)g(z)g(z+c)+B(z), $$ where A ( z ) $A(z)$ and B ( z ) $B(z)$ are polynomials such that deg A ( z ) > 0 $\deg A(z)>0$ , then 1 ≤ ρ ( g ) = max { λ ( g ) , λ ( 1 g ) } . $$1 \leq\rho(g)=\max\biggl\{ \lambda(g), \lambda\biggl(\frac{1}{g}\biggr) \biggr\} . $$ |
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| ISSN: | 1687-1847 |