The aim of this study is to examine some numerical tests of Pad�´e approximation for some typical functions with singularities such\nas simple pole, essential singularity, brunch cut, and natural boundary. As pointed out by Baker, it was shown that the simple pole\nand the essential singularity can be characterized by the poles of the Pad�´e approximation. However, it was not fully clear how the\nPad�´e approximation works for the functions with the branch cut or the natural boundary. In the present paper, it is shown that the\npoles and zeros of the Pad�´e approximated functions are alternately lined along the branch cut if the test function has branch cut, and\npoles are also distributed around the natural boundary for some lacunary power series and random power series which rigorously\nhave a natural boundary on the unit circle. On the other hand, Froissart doublets due to numerical errors and/or external noise\nalso appear around the unit circle in the Pad�´e approximation. It is also shown that the residue calculus for the Pad�´e approximated\nfunctions can be used to confirm the numerical accuracy of the Pad�´e approximation and quasianalyticity of the random power\nseries.
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