Hello everyone:
I'm trying to get particular coefficients from taylor series expansions.
So, I start with the function f(x1,x2) = 1/(1 - x2*x1^t), and I take the
taylor series expansion at x1 = 1, and then I would like the coefficient on
the 1/(1-x1) term. However, when I do this, I get two different results,
based off of whether I expand at x2 = 1 and Then expand at x1 = 1, or if I
only expand at x1 = 1. Here is the code and the results:
#here I expand at x2 = 1 first, and then at x1 = 1, and then I find the
coefficient at 1/(x1-1) and subtitute in x2 = 1 at the end to simplify the
output
sage: x1,x2,t = var('x1,x2,t')
sage: ((1/(1-x1^t)).taylor(x2,1,4).taylor(x1,1,4).coefficient(1/(x1-1))).
substitute(x2=1)
-1/t
#here I only expand at x1 = 1, then look for the coefficient.
sage: x1,x2,t = var('x1,x2,t')
sage: ((1/(1-x2*x1^t)).taylor(x1,1,4)).coefficient(1/(x1-1)).substitute(x2=1
)
0
The former gives me -1/t and the latter gives me 0. I would have thought
that the two taylor series were equivalent, no? What am I missing? Thanks!
-Saad
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