Geodesic
The domain of regularity of the limit function of a sequence of analytic functions
Matematičeskie zametki, Tome 12 (1972) no. 6, pp. 681-692 
V. V. Napalkov. The domain of regularity of the limit function of a sequence of analytic functions. Matematičeskie zametki, Tome 12 (1972) no. 6, pp. 681-692. http://geodesic.mathdoc.fr/item/MZM_1972_12_6_a4/
@article{MZM_1972_12_6_a4,
     author = {V. V. Napalkov},
     title = {The domain of regularity of the limit function of a sequence of analytic functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {681--692},
     year = {1972},
     volume = {12},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_6_a4/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $f(z)$ be an entire function $\lambda_n$ ($n=0,1,2,\dots$) complex numbers, such that the system $\{f(\lambda_nz)\}_{n=0}^\infty$ is not complete in the circle $|z| and let the sequence $Q_n(z)$ have the form $\sum_{k=0}^{p_n}a_{nk}f(\lambda_k\cdot z)$. We study the properties of the limit function of the sequence $Q_n(z)$ in the case when $$ f(z)=1+\sum_{n=1}^\infty\frac{z^n}{P(1)P(2)\dots P(n)}, $$ where $P(z)$ is a polynomial having at least one negative integral root.