GenerateUnivariatePowerSeries2(FE)

genups.spad line 117 [edit on github]

• FE : Join(Ring, RetractableTo(Symbol))

GenerateUnivariatePowerSeries provides functions that create power series from explicit formulas for their nth coefficient.

laurent : (FE, Symbol, Equation(FE), UniversalSegment(Integer)) -> Any if FE has Evalable(FE) and FE has RetractableTo(Integer)

laurent(a(n), n, x=a, n0..) returns sum(n = n0.., a(n) * (x - a)^n); laurent(a(n), n, x=a, n0..n1) returns sum(n = n0..n1, a(n) * (x - a)^n).

laurent : (Mapping(FE, Integer), Equation(FE), UniversalSegment(Integer)) -> Any

laurent(n +-> a(n), x = a, n0..) returns sum(n = n0.., a(n) * (x - a)^n); laurent(n +-> a(n), x = a, n0..n1) returns sum(n = n0..n1, a(n) * (x - a)^n).

puiseux : (FE, Symbol, Equation(FE), UniversalSegment(Fraction(Integer)), Fraction(Integer)) -> Any if FE has Evalable(FE) and FE has RetractableTo(Fraction(Integer))

puiseux(a(n), n, x = a, r0.., r) returns sum(n = r0, r0 + r, r0 + 2*r..., a(n) * (x - a)^n); puiseux(a(n), n, x = a, r0..r1, r) returns sum(n = r0 + k*r while n <= r1, a(n) * (x - a)^n).

puiseux : (Mapping(FE, Fraction(Integer)), Equation(FE), UniversalSegment(Fraction(Integer)), Fraction(Integer)) -> Any

puiseux(n +-> a(n), x = a, r0.., r) returns sum(n = r0, r0 + r, r0 + 2*r..., a(n) * (x - a)^n); puiseux(n +-> a(n), x = a, r0..r1, r) returns sum(n = r0 + k*r while n <= r1, a(n) * (x - a)^n).

series : (FE, Symbol, Equation(FE)) -> Any if FE has Evalable(FE) and FE has RetractableTo(Fraction(Integer))

series(a(n), n, x = a) returns sum(n = 0.., a(n)*(x-a)^n).

series : (FE, Symbol, Equation(FE), UniversalSegment(Fraction(Integer)), Fraction(Integer)) -> Any if FE has Evalable(FE) and FE has RetractableTo(Fraction(Integer))

series(a(n), n, x = a, r0.., r) returns sum(n = r0, r0 + r, r0 + 2*r..., a(n) * (x - a)^n); series(a(n), n, x = a, r0..r1, r) returns sum(n = r0 + k*r while n <= r1, a(n) * (x - a)^n).

series : (FE, Symbol, Equation(FE), UniversalSegment(Integer)) -> Any if FE has Evalable(FE) and FE has RetractableTo(Fraction(Integer))

series(a(n), n, x=a, n0..) returns sum(n = n0.., a(n) * (x - a)^n); series(a(n), n, x=a, n0..n1) returns sum(n = n0..n1, a(n) * (x - a)^n).

series : (Mapping(FE, Fraction(Integer)), Equation(FE), UniversalSegment(Fraction(Integer)), Fraction(Integer)) -> Any

series(n +-> a(n), x = a, r0.., r) returns sum(n = r0, r0 + r, r0 + 2*r..., a(n) * (x - a)^n); series(n +-> a(n), x = a, r0..r1, r) returns sum(n = r0 + k*r while n <= r1, a(n) * (x - a)^n).

series : (Mapping(FE, Integer), Equation(FE)) -> Any

series(n +-> a(n), x = a) returns sum(n = 0.., a(n)*(x-a)^n).

series : (Mapping(FE, Integer), Equation(FE), UniversalSegment(Integer)) -> Any

series(n +-> a(n), x = a, n0..) returns sum(n = n0.., a(n) * (x - a)^n); series(n +-> a(n), x = a, n0..n1) returns sum(n = n0..n1, a(n) * (x - a)^n).

taylor : (FE, Symbol, Equation(FE)) -> Any if FE has Evalable(FE) and FE has RetractableTo(Integer)

taylor(a(n), n, x = a) returns sum(n = 0.., a(n)*(x-a)^n).

taylor : (FE, Symbol, Equation(FE), UniversalSegment(NonNegativeInteger)) -> Any if FE has Evalable(FE) and FE has RetractableTo(Integer)

taylor(a(n), n, x = a, n0..) returns sum(n = n0.., a(n)*(x-a)^n); taylor(a(n), n, x = a, n0..n1) returns sum(n = n0.., a(n)*(x-a)^n).

taylor : (Mapping(FE, Integer), Equation(FE)) -> Any

taylor(n +-> a(n), x = a) returns sum(n = 0.., a(n)*(x-a)^n).

taylor : (Mapping(FE, Integer), Equation(FE), UniversalSegment(NonNegativeInteger)) -> Any

taylor(n +-> a(n), x = a, n0..) returns sum(n=n0.., a(n)*(x-a)^n); taylor(n +-> a(n), x = a, n0..n1) returns sum(n = n0.., a(n)*(x-a)^n).