A~property of entire functions with real taylor coefficients
Matematičeskie zametki, Tome 18 (1975) no. 3, pp. 395-402
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Suppose that $f(z)$ is an entire transcendental function with real Taylor coefficients, $M(r)=max|f(z)|$ on $|z|=r$, and $\{\lambda_n\}$ is the sequence of sign changes of the coefficients. We will show that if $\sum(1/\lambda_n)\infty$, then $\overline{\lim\limits_{r\to\infty}}\ln\cdot|f(r)|/\ln M(r)=1$.
@article{MZM_1975_18_3_a7,
author = {M. N. Sheremeta},
title = {A~property of entire functions with real taylor coefficients},
journal = {Matemati\v{c}eskie zametki},
pages = {395--402},
publisher = {mathdoc},
volume = {18},
number = {3},
year = {1975},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_3_a7/}
}
M. N. Sheremeta. A~property of entire functions with real taylor coefficients. Matematičeskie zametki, Tome 18 (1975) no. 3, pp. 395-402. http://geodesic.mathdoc.fr/item/MZM_1975_18_3_a7/