1
vote
2answers
119 views

Expansion with binomial coefficients

How can I get binomial coefficients in expansion of $(n x+i) (1+i x)^n+(n x-i) (1-i x)^n$, where $i=\sqrt{-1}$ and $n$ is an integer. I have no idea how to coax Mathematica to do something remotely ...
2
votes
0answers
104 views

Changing bounds of summation after differentiating symbolic sums

Suppose, I have a function written as Taylor-Maclaurin series f = Sum[c[n]*x^n, {n, 0, Infinity}] Now, I wish to differentiate this expression with respect to ...
9
votes
2answers
445 views

Find closed form expression for series expansion coefficients [duplicate]

Is there a built-in function that will find a general expression for the coefficient of the series expansion of a function? Series will only give the explicit ...
6
votes
1answer
168 views

Sophistication of Series[…]

I'll give a concrete example and I hope that my general question will be clear. Say I have three variables, $f$, $g$, $h$, and I know that $f=\mathcal O(x)$, $g=\mathcal O(x^2)$, $h=\mathcal O(x^3)$ ...