Geodesic
Convergence of Pad\'e approximations
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (1982), pp. 3-6

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If a function $f$ is holomorphic in the circle $\{|z|1\}$ and its Padé approximants have no poles in that circle then these approximants uniformly converge to $f$ in any circle with radius less than $0{,}583$. 
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     author = {A. V. Vyatchin},
     title = {Convergence of {Pad\'e} approximations},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
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     publisher = {mathdoc},
     number = {4},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_4_a0/}
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A. V. Vyatchin. Convergence of Pad\'e approximations. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (1982), pp. 3-6. http://geodesic.mathdoc.fr/item/VMUMM_1982_4_a0/