GenerateUnivariatePowerSeries1(R)

genups.spad line 1 [edit on github]

• R : Ring

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

laurent : (Mapping(R, Integer), 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 : (Mapping(R, Fraction(Integer)), 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 : (Mapping(R, Integer), Symbol, R) -> Any

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

taylor : (Mapping(R, Integer), 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).