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Given a function f and two integers m ≥ 0 and n ≥ 0, the Padé approximant of order (m, n) is the rational function R ( x ) = p 0 + p 1 x + p 2 x 2 + ⋯...

Gauge00's derivation, it is from the original derivation Householder's method. An exact derivation of the Householder's methods starts from the Padé approximation...