Hi,
I get with Maple:
LargeSchroeder := (1 - x - sqrt(1 - 6*x + x^2))/(2*x);
series(LargeSchroeder, x, 6);
taylor(LargeSchroeder, x=0, 6);
1+2*x+6*x^2+22*x^3+90*x^4+394*x^5+O(x^6)
1+2*x+6*x^2+22*x^3+90*x^4+394*x^5+O(x^6)
Both functions give the same result. Not so with Sage.
With Sage 8.4:
LargeSchroeder = SR((1 - x - sqrt(1 - 6*x + x^2))/(2*x))
print(LargeSchroeder.taylor(x, 0, 6).list())
print(LargeSchroeder.series(x, 6).list())
[1, 2, 6, 22, 90, 394, 1806]
[3/2, 2, 6, 22, 90, 394]
Bug or feature? Moreover
taylor? .. gives hints
series? .. Object `series` not found.
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