PadeApproximantPackage(R, x, pt)

pade.spad line 1 [edit on github]

• R: Field

• x: Symbol

• pt: R

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).