# Questions tagged [series-expansion]

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

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### Expanding elliptic function of third kind

I want to expand an elliptic function of third kind in terms of $g$, where $n$, $\psi$, and $k$ are functions of $g$. For example, I defined ...
64 views

### Series expansion for ProductLog[-1,x]

Is there a way to get Mathematica to expand Series[ProductLog[-1, x], {x, -Exp[-1], 1}]? I'm on Mathematica 12, and it just returns ...
78 views

### Series of a product of series

I am writing a code where I have to multiply large series truncated at some order, say 100. As a result I want again a series up to order 100, and I want to get it in the fastest way. I have tried a ...
98 views

### Coefficient of power $p$ in polynomial expansion : Mathematica doesn't answer me

I would like to compute the coefficient in front of $n^p$ for a polynomial expansion. I wrote the following code: ...
67 views

### Asymptotic series : why doesn't Mathematica compute it in power of $1/x$?

Consider the following : Series[Cos[Pi/2*Sqrt[n/x]] - Cos[Pi/2*Sqrt[(n + 1)/x]], {x, Infinity, 2}] I expect mathematica to find me the $1/x$ perturbative ...
23 views

### Showing step-by-step answers for power series identities?

We have Sum[1/n^2, {n, 1, Infinity}] (* Evaluate to Pi^2/6 *) ..but is there a way to show how this is derived step-by-step? NOTE: I have seen step-by-step ...
A very simple question: How can I tell to Mathematica that: $$$x*\sum_{k=0}^{\infty}\,b_kx^k=\sum_{k=0}^{\infty}\,b_kx^{k+1}$$$ I tried to multiply but Mathematica gives ...