gives the Padé approximant to expr about the point x=x0, with numerator order m and denominator order n.
gives the diagonal Padé approximant to expr about the point x=x0 of order n.
- The Wolfram Language can find the Padé approximant about the point x=x0 only when it can evaluate power series at that point.
- PadeApproximant produces a ratio of ordinary polynomial expressions, not a special SeriesData object.
Examplesopen allclose all
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:
Generalizations & Extensions (3)
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:
Properties & Relations (2)
The Padé approximant agrees with the ordinary series for terms:
For PadeApproximant gives an ordinary series:
Possible Issues (2)
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: