Geodesic
On the analytic continuation of functions defined by regrouped power series
Matematičeskie zametki, Tome 15 (1974) no. 5, pp. 683-690.

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We consider functions defined by regrouped power series $f(z)=\sum_{n=0}^\infty z^{\lambda_n}P_{k_n}(z)$ in the disk $|z|1$ and also in some domain $D$ outside of this disk. We obtain conditions under which $f(z)$ is analytically continuable outside of the disk $|z|1$, the analytic continuation being effected with the help of the given series. We also consider the analytic continuability of functions $f(z,w)$. 
@article{MZM_1974_15_5_a3,
     author = {V. A. Belyaev},
     title = {On the analytic continuation of functions defined by regrouped power series},
     journal = {Matemati\v{c}eskie zametki},
     pages = {683--690},
     publisher = {mathdoc},
     volume = {15},
     number = {5},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_5_a3/}
}
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V. A. Belyaev. On the analytic continuation of functions defined by regrouped power series. Matematičeskie zametki, Tome 15 (1974) no. 5, pp. 683-690. http://geodesic.mathdoc.fr/item/MZM_1974_15_5_a3/