Abstract
We present some results on the periodicity of an entire function f(z) with its differential-difference polynomials. For instance, we obtain that if fn + L(f) is a periodic function with period c, then f(z) must be a periodic function with period c, where f(z) is a transcendental entire function with hyper-order less than one and \(N(r,{1 \over f}) = S(r,f),\,L(f)\) is a differential-difference polynomial in f with constant coefficients and degree less than n.
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Authors would like to thank Prof Kai Liu and the reviewer for useful comments and discussions.
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This work was supported by the NSFC (No. 12061042) and by Jiangxi Provincial Natural Science Foundation (No. 20202BAB201003).
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Liu, X.L., Wei, Y.M. The periodicity of differential-difference polynomials of entire functions. Anal Math 48, 127–138 (2022). https://doi.org/10.1007/s10476-022-0119-9
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DOI: https://doi.org/10.1007/s10476-022-0119-9