# PadeApproximantPackage(R, x, pt)ΒΆ

This package computes reliable Pad&ea. approximants using a generalized Viskovatov continued fraction algorithm. Authors: Trager, Burge, Hassner & Watt. Date Created: April 1987 Keywords: Pade, series Examples: References: “Pade Approximants, Part I: Basic Theory”, Baker & Graves-Morris.

- pade: (NonNegativeInteger, NonNegativeInteger, UnivariateTaylorSeries(R, x, pt)) -> Union(Fraction UnivariatePolynomial(x, R), failed)
`pade(nd, dd, s)`

computes the quotient of polynomials (if it exists) with numerator degree at most`nd`

and denominator degree at most`dd`

which matches the series`s`

to order`nd + dd`

.

- pade: (NonNegativeInteger, NonNegativeInteger, UnivariateTaylorSeries(R, x, pt), UnivariateTaylorSeries(R, x, pt)) -> Union(Fraction UnivariatePolynomial(x, R), failed)
`pade(nd, dd, ns, ds)`

computes the approximant as a quotient of polynomials (if it exists) for arguments`nd`

(numerator degree of approximant),`dd`

(denominator degree of approximant),`ns`

(numerator series of function), and`ds`

(denominator series of function).