pade(): rational approximation from a series

pade() builds a Padé approximation: a ratio of two polynomials chosen to match terms of a power series. Rational approximations can represent poles and often behave better than a truncated polynomial away from the expansion point.

When it helps

Use Padé approximation for symbolic analysis, control models, and numerical estimates where a Taylor series converges slowly. Select numerator and denominator orders based on the available series and the desired behavior.

Related functions

Use derivative() to obtain series information, simplify() to reduce the rational result, resolve() to inspect poles, and numeric() to compare approximations.

Caveat

A Padé approximant is not automatically accurate everywhere. Check it near singularities and against the original function over the range you actually need.