Rows and diagonals of the Walsh array for entire functions with smooth Maclaurin series coefficients

1990 ◽  
Vol 6 (3) ◽  
pp. 257-286 ◽  
Author(s):  
A. L. Levin ◽  
D. S. Lubinsky
Keyword(s):  
Entire Functions ◽  
Maclaurin Series ◽  
Walsh Array

scholarly journals Uniqueness on entire functions and their nth order exact differences with two shared values

2020 ◽  
Vol 18 (1) ◽  
pp. 211-215
Author(s):  
Shengjiang Chen ◽  
Aizhu Xu
Keyword(s):  
Entire Function ◽  
Entire Functions ◽  
Shared Values ◽  
Simple Method ◽  
Exact Difference ◽  
Hyper Order

Abstract Let f(z) be an entire function of hyper order strictly less than 1. We prove that if f(z) and its nth exact difference {\Delta }_{c}^{n}f(z) share 0 CM and 1 IM, then {\Delta }_{c}^{n}f(z)\equiv f(z) . Our result improves the related results of Zhang and Liao [Sci. China A, 2014] and Gao et al. [Anal. Math., 2019] by using a simple method.

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