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Uniqueness on Linear Differential-Difference Polynomials
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DOI：10.3103/S1068362325600515.png)
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Abstract
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In this article, let g(z) be a meromorphic function of rho(2)(g) < 1. Suppose that a linear differential-difference polynomial of the form P(z,g) = (n)Sigma (k=1) b(k)(z)g(z + c(k)) +(m)Sigma (k=1 )d(k)(z)g((k)) (z + alpha(k)) +(p)Sigma (k=1) t(k)(z)g((k)) (z), where n, m, p >= 1 and b(k)(z), d(k)(z), t(k)(z) are nonzero small functions relative to g(z), and c(k), alpha(k) are distinct complex numbers. We study the uniqueness problems of g(z) and P(z,g). Meantime we obtain some results related to the complex differential-difference equations with a more general form than the previous equations given by Zhang et al. [1].
Keywords:
meromorphic function
linear differential-difference polynomial
uniqueness
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