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Definition Given a function f and two integer s m ≥ 0 and n ≥ 0 , the Padé approximant of order [ m/n ] is the rational function which agrees with f ( x ) to the highest possible order , which amounts to Equivalently , if R ( x ) is expanded in a Maclaurin series ( Taylor series at 0 ) , its first m + n terms would cancel the first m + n terms of f ( x ) , and as such : The Padé approximant is unique for given m and n , that is , the coefficients a_0 , a_1 , \ dots , a_m , b_1 , \ dots , b_n can be uniquely determined .
 Padé, Padé
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 Padé, Padé