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Upgrading from:

Calculus`Pade`

PadeApproximant has been added to the built-in Mathematica kernel.
EconomizedRationalApproximation is now available in the newly created Function Approximations Package.

PadeApproximant

Syntax for PadeApproximant has changed from the Pade function in Calculus`Pade`:

Version 5.2 << Calculus`Pade` Pade[Cos[x], {x, 0, 4, 4}]

The Padé approximant of Cos[x] about the point x=0 with numerator of degree 2 and denominator of degree 4:

Wolfram Language code: PadeApproximant[Cos[x], {x, 0, {2, 4}}]

This finds the diagonal Padé approximant of order 4:

Version 5.2 Pade[Cos[x], {x, 0, 2, 4}]
Wolfram Language code: PadeApproximant[Cos[x], {x, 0, 4}]

EconomizedRationalApproximation

To access functionality from the new Function Approximations Package, load FunctionApproximations`:

Version 5.2 << Calculus`Pade`
Wolfram Language code: <<FunctionApproximations`

Syntax for EconomizedRationalApproximation is the same as in Calculus`Pade` in Version 5.2. Here is the economized rational approximation of degree (2,4) of ex over the interval 0≤x≤2:

Wolfram Language code: era = EconomizedRationalApproximation[Exp[x], {x, {0, 2}, 2, 4}]