In [mathematics](https://en.wikipedia.org/wiki/Mathematics "Mathematics"), a Padé approximant is the "best" approximation of a function by a [rational function](https://en.wikipedia.org/wiki/Rational_function "Rational function") of given order – under this technique, the approximant's [power series](https://en.wikipedia.org/wiki/Power_series "Power series") agrees with the power series of the function it is approximating. The technique was developed around 1890 by [Henri Padé](https://en.wikipedia.org/wiki/Henri_Pad%C3%A9 "Henri Padé"), but goes back to [Georg Frobenius](https://en.wikipedia.org/wiki/Georg_Frobenius "Georg Frobenius"), who introduced the idea and investigated the features of rational approximations of power series.

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Author of the notes: Antonio J. Pan-Collantes

antonio.pan@uca.es