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Pad\'e approximants are rational functions whose series expansion match agiven series as far as possible. These approximants are usually written under arational form. In this paper, we will show how to write them also under twodifferent barycentric forms, and under a partial fraction form, depending onfree parameters. According to the choice of these parameters, Pad\'e-typeapproximants can be obtained under a barycentric or a partial fraction form.

New representations of Pad\'e and Pad\'e-type approximants