Padé Approximants

• is the "best" approximation of a function near a specific point by a rational function of a given order

Definition

Given a function 𝑓 and two integers 𝑚≥0 and 𝑛≥1, the Padé approximant of order [𝑚/𝑛] is the rational function:

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which agrees with 𝑓(𝑥) to the highest possible order, which amounts to

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Introduction