ExpressionToUnivariatePowerSeries(R, FE)

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 -> 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.

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 : Symbol -> Any

laurent(x) returns x viewed as a Laurent series.

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.

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 : Symbol -> Any

puiseux(x) returns x viewed as a Puiseux series.

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.

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 : Symbol -> Any

series(x) returns x viewed as a series.

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.

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 : Symbol -> Any

taylor(x) returns x viewed as a Taylor series.