BUILT-IN MATHEMATICA SYMBOL

PadeApproximant

gives the Padé approximant to expr about the point

, with numerator order m and denominator order n.

gives the diagonal Padé approximant to expr about the point

of order n.

Mathematica can find the Padé approximant about the point only when it can evaluate power series at that point.

PadeApproximant produces a ratio of ordinary polynomial expressions, not a special SeriesData object.

Order [2/3] Padé approximant for Exp[x]:

PadeApproximant can handle functions with poles:

Order [2/3] Padé approximant for Exp[x]:

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PadeApproximant can handle functions with poles:

Out[1]=

Padé approximant of an arbitrary function:

Padé approximant with a complex-valued expansion point:

Padé approximant with an expansion point at infinity:

Find a Padé approximant to a given series:

Padé approximant centered at the point

:

Padé approximant in fractional powers:

Padé approximant of a function containing logarithmic terms:

Plot successive Padé approximants to

:

Construct discrete orthogonal polynomials with respect to discrete weighted measure:

The Padé approximant agrees with the ordinary series for

terms:

For

PadeApproximant gives an ordinary series:

Padé approximants often have spurious poles not present in the original function:

Padé approximants of a given order may not exist:

Perturbing the order slightly is usually sufficient to produce an approximant: