# Questions tagged [series-expansion]

Questions on dealing with series data and constructing power series expansions of functions.

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### Expand series unevaluated

I'm newbie in Mathematica. I'd like to obtain nice and verbose output for any series calculation. For example, given a simple sequence n*(-1)^(n-1) and ...
5k views

### Laurent series expansion

Can someone share how to find the Laurent series expansion of $$f(z)=\frac{1}{(z^2-1)(z^2-4)}$$ centered at $0$ on the annulus $1<|z|<2$?
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### Bug in SumConvergence

Bug introduced in 10.0.1 and fixed in 12.0.0 Version 11.2.0.0 on MacBook Pro: ...
2k views

### Finding the coefficient of a certain power in a generating function

I want to compute $(t^1+\dots +t^5)(t^2+\dots+ t^6)(t^3+\dots +t^9)$ and find the coefficient of $t^{15}$ for example. $t$ is an indeterminate Now in Maple this is simply as ...
535 views

### Declaration of abstract matrices to perform series expansion on them

I would like to have abstract matrices M and S to get out the coefficients of matrix power series however it treats M and S as numbers even if i checked that M.S - S.M != 0. I attach my code below: <...
447 views

### Generating terms of the Stirling series

The Stirling series starts as follows: n!=\left(\frac{n}{e}\right)^{n}\sqrt{2\pi n} \left\{1+\frac{1}{12n}+\frac{1}{288n^{2}}-\frac{139}{51840 n^{3}}-\frac{571}{2888380 n^{4}}+O\left(n^{-5}\right)\...
469 views

### Series expansion wrong

I had to work with some series expansions lately, and at some point I realised that something was becoming inconsistent at some point. It seems that applying Factor ...
288 views

### How to represent $f(x) = (y-x)^k \log(y-x)$ as a summation of the form $f(x) = \sum\limits_{j=0}^\infty \cdots$?

I am having a lot of trouble working with summations in Mathematica, and this is unfortunate as it is my main use case for the application My latest summation issue is the following. I am trying to ...
For the following Cauchy problem of a non linear ODE: \begin{equation} \ddot{x}=-|x|^{1/3} \end{equation} which satisfies the initial conditions $x(0)=1, \dot{x}(0)=0$, I am aware that there are ...
I'm looking for an analytical approximation of $\int_a^b e^{-x^2}\mathrm{erf}(x+c) dx$ that would be accurate to precision $\varepsilon$ for $a,b,c$ within a certain range. How do I ask Mathematica ...