# ExpressionToUnivariatePowerSeries(R, FE)ΒΆ

expr2ups.spad line 1 [edit on github]

R: Join(GcdDomain, Comparable, RetractableTo Integer, LinearlyExplicitOver Integer)

FE: Join(AlgebraicallyClosedField, TranscendentalFunctionCategory, FunctionSpace R)

This package provides functions to convert functional expressions to power series.

- laurent: (FE, Equation FE) -> Any
`laurent(f, x = a)`

expands the expression`f`

as a Laurent series in powers of`(x - a)`

.

- laurent: (FE, Equation FE, Integer) -> Any
`laurent(f, x = a, n)`

expands the expression`f`

as a Laurent series in powers of`(x - a)`

; terms will be computed up to order at least`n`

.

- laurent: (FE, Integer) -> Any
`laurent(f, n)`

returns a Laurent expansion of the expression`f`

. Note:`f`

should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least`n`

.

- laurent: FE -> Any
`laurent(f)`

returns a Laurent expansion of the expression`f`

. Note:`f`

should have only one variable; the series will be expanded in powers of that variable.

- puiseux: (FE, Equation FE) -> Any
`puiseux(f, x = a)`

expands the expression`f`

as a Puiseux series in powers of`(x - a)`

.

- puiseux: (FE, Equation FE, Fraction Integer) -> Any
`puiseux(f, x = a, n)`

expands the expression`f`

as a Puiseux series in powers of`(x - a)`

; terms will be computed up to order at least`n`

.

- puiseux: (FE, Fraction Integer) -> Any
`puiseux(f, n)`

returns a Puiseux expansion of the expression`f`

. Note:`f`

should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least`n`

.

- puiseux: FE -> Any
`puiseux(f)`

returns a Puiseux expansion of the expression`f`

. Note:`f`

should have only one variable; the series will be expanded in powers of that variable.

- series: (FE, Equation FE) -> Any
`series(f, x = a)`

expands the expression`f`

as a series in powers of (`x`

- a).

- series: (FE, Equation FE, Fraction Integer) -> Any
`series(f, x = a, n)`

expands the expression`f`

as a series in powers of (`x`

- a); terms will be computed up to order at least`n`

.

- series: (FE, Fraction Integer) -> Any
`series(f, n)`

returns a series expansion of the expression`f`

. Note:`f`

should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least`n`

.

- series: FE -> Any
`series(f)`

returns a series expansion of the expression`f`

. Note:`f`

should have only one variable; the series will be expanded in powers of that variable.

- taylor: (FE, Equation FE) -> Any
`taylor(f, x = a)`

expands the expression`f`

as a Taylor series in powers of`(x - a)`

.

- taylor: (FE, Equation FE, NonNegativeInteger) -> Any
`taylor(f, x = a)`

expands the expression`f`

as a Taylor series in powers of`(x - a)`

; terms will be computed up to order at least`n`

.

- taylor: (FE, NonNegativeInteger) -> Any
`taylor(f, n)`

returns a Taylor expansion of the expression`f`

. Note:`f`

should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least`n`

.

- taylor: FE -> Any
`taylor(f)`

returns a Taylor expansion of the expression`f`

. Note:`f`

should have only one variable; the series will be expanded in powers of that variable.