Geodesic
Conditions for the representability of analytic functions by series of rational functions
Matematičeskie zametki, Tome 15 (1974) no. 2, pp. 197-203.

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With a function $f(z)$, analytic in the unit circle, we associate by a specific rule the series $\sum_{n=1}^\infty\frac{A_n}{a-\lambda_nz}$, $|\lambda_n|1$. We derive a (necessary and sufficient) condition for the convergence of the series in the unit circle. We derive further conditions under which the series converges to the function $f(z)$ itself. 
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     author = {T. A. Leont'eva},
     title = {Conditions for the representability of analytic functions by series of rational functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {197--203},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_2_a2/}
}
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T. A. Leont'eva. Conditions for the representability of analytic functions by series of rational functions. Matematičeskie zametki, Tome 15 (1974) no. 2, pp. 197-203. http://geodesic.mathdoc.fr/item/MZM_1974_15_2_a2/