GenerateUnivariatePowerSeries2 FEΒΆ

genups.spad line 117 [edit on github]

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: (Integer -> FE, 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: (Fraction Integer -> FE, 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: (Fraction Integer -> FE, 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: (Integer -> FE, Equation FE) -> Any

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

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

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

taylor: (Integer -> FE, 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).