GenerateUnivariatePowerSeries1 R

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• R: Ring

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

laurent: (Integer -> R, Symbol, R, 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: (Fraction Integer -> R, Symbol, R, 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).

taylor: (Integer -> R, Symbol, R) -> Any

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

taylor: (Integer -> R, Symbol, R, 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).