# GenerateUnivariatePowerSeries(R, FE)ΒΆ

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

laurent: (FE, Symbol, Equation FE, UniversalSegment Integer) -> Any
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
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
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
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
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
taylor(a(n), n, x = a) returns sum(n = 0.., a(n)*(x-a)^n).
taylor: (FE, Symbol, Equation FE, UniversalSegment NonNegativeInteger) -> Any
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).