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PadeApproximant

PadeApproximant[expr, {x, x₀, {m, n}}]
gives the Padé approximant to expr about the point x=x₀, with numerator order m and denominator order n.

PadeApproximant[expr, {x, x₀, n}]
gives the diagonal Padé approximant to expr about the point x=x₀ of order n.

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Mathematica can find the Padé approximant about the point x=x₀ only when it can evaluate power series at that point.

PadeApproximant produces a ratio of ordinary polynomial expressions, not a special SeriesData object.

Basic Examples (2)

Order [2/3] Padé approximant for Exp[x]:

PadeApproximant can handle functions with poles:

Generalizations & Extensions (3)

Applications (2)

Properties & Relations (2)

Possible Issues (2)

Series Rationalize

Padé Approximation

Rational Functions

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