# Tagged Questions

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

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### Evaluation of a triple sum does not finish in reasonable time

I'm trying to compute the following triple sum, but no result is produced within a reasonable amount of time. What to do? ...
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### Decimal representations of analytic values in an expansion

I have a solution to an ODE (which I call sol), which I would like to expand in terms of Log[1+x] around x=-1. I thought that: ...
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### 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: <...
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### The proper way to write the input for a certain series

Mathematica tells the series below doesn't converge. I think it converges. What would the proper way to write things be as an input? ...
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### How can we suppress the asymptotic notation in Series? [closed]

Series expands a function, and also gives an idea of the asymptotic bounds of the function: Series[$\frac{1-x^3}{1-x}$] returns: $1 + x + x^2 + O(x)^5$ I'd like ...
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### Laurent series expansion

Can someone share how to find a Laurent series expansion of $$f(z)=\frac{1}{(z^2-1)(z^2-4)}$$ centered at zero on the annular disk $1<|z|<2$?
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### Why does Mathematica fail to series expand this simple expression?

I wanted to expand the function $(x+2)^{x+2}$ around $x = -1$, that is, using Series[(x + 2)^(x + 2), {x, -1, 2}] and Mathematica returns the same expression. ...
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### Design considerations behind O (a.k.a. BigOh, a.k.a. Landau Order)

This works without any warnings: O[Log[x]]. This raises a warning: O[x^2]. I have a few questions around this: Why is it a ...
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### Series expansion in terms of Hermite polynomials

I am trying to expand a polynomial in terms of orthogonal polynomials (in my case, Hermite). Maple has a nice built-in function for this, ChangeBasis. Is there a ...
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### Calculating Taylor polynomial of an implicit function given by an equation

I'd like to write a procedure that will take an equation: F(x,y,z) = 0 chosen variable: x a point: ...
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### Getting poles of a Gamma functions [duplicate]

Why do the following 2 sequences give different answers? n = 1.5 Series[Gamma[0.5 - n - x], {x, 0, 2}] Series[Gamma[-1 - x], {x, 0, 2}] (..clearly the output from the second expression is ...
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### Expansion of $E(i c \mid m)$ at $c\to\infty$?

Currently, I am using a Windows machine with Mathematica 8. I noticed a difference in a series expansion of the function EllipticE[] in comparison with a result ...
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### Expansion in Basis Functions

I am trying to create an expansion of the form f[x,y]->Sum[Cn[x] y^n,{n,1,order}] To replace the function f by the ...
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### Asymptotic expansion of a list

I am trying to calculate a asymptotic series expansion of a list. ...
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### Unexpected behaviour of SeriesCoefficient?

Following this question/answer I discovered and played with SeriesCoefficient. In particular, I tried ...
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### 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 ...
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### Formatting Equation Output Neatly

I looked around and couldn't find the answer to this anywhere, so I'm sorry if this is a bad question - I'm pretty new to mathematica. I wrote a program to help me compute some annoying series ...
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### Proper treatment of roots and powers in Series?

I have the following problem in Mathematica 9 on Linux. I let Mathematica compute the Series expansion: ...
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### How do I solve N simultaneous equations for N variables?

I have a function: f[x_] := x + 31 x^3 + 5 x^25 Which I want to find an expansion for: ...
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### Series command no longer expands arbitrary functions after aborting previous evaluation

I asked Mathematica 9 to execute the SeriesCoefficient command on a rather horrendously complicated expression. After some time I decided to abort the evaluation ...
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### Asymptotic expansion, negative powers

The question was inspired by this discussion: How to expand a function into a power series with negative powers? I am interested in asymptotic behavior of a function at infinity: ...
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### Why does $\frac{\partial}{\partial x}O\left(\left(\frac{1}{x}\right)^0\right)$ equal $O\left(\left(\frac{1}{x}\right)^0\right)$ in a series expansion?

When taking the derivative of a series expansion around a finite point, the $O(x^n)$ part is differentiated as expected. $O(x^n)$ becomes $O(x^{n-1})$ except $O(x^0)$ which stays $O(x^0)$. When ...
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### How to study asymptotic behavior, built-in functions

My question is as follows. Suppose we have a function $f(r)$ and we want to study its asymptotic behavior at infinity ($r\rightarrow \infty$). For example, the function may reduce to $-\frac{a}{r}$ or ...
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### How to expand a function into a power series with negative powers?

Is there any way to expand this expression a+b(1-Exp[-T/(b c)]/(z-Exp[-T/ (b c)]) (where a, ...
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### Multivariable Taylor expansion does not work as expected

The basic multivariable Taylor expansion formula around a point is as follows:  f(\mathbf r + \mathbf a) = f(\mathbf r) + (\mathbf a \cdot \nabla )f(\mathbf r) + \frac{1}{2!}(\mathbf a \cdot \nabla)...
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### How can I get a Taylor expansion of the Sin[x] function?

How can I get a Taylor expansion of the Sin[x] function by the power series?
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For an arbitrary function $f(x,y)$ I am defining functions LogMT1 and LogMT2 as follows, ...
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I want to be able to do high dimensional integrals like, (..naively I wrote it as this..) ...
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### Series expansion with irrational power

I need the series expansion of a fairly nasty function and its derivative: ...
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### Limiting form of a polynomial expression

When simplifying an expression by hand, a trick that is often used is to remove terms that are lower powers of the independent variable, for instance, as $x \rightarrow \infty$, $x^2 + x$ becomes ...
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### Fourier series of interpolating function result of NDSolve

I am having a tough time formulating the right question but here goes. I know that solving the pde as in here gives me an interpolating function. I understand that the interpolating function object ...
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 $f=\mathcal O(x)$, $g=\mathcal O(x^2)$, $h=\mathcal O(x^3)$ (...
I have to find the series expansion of the inverse function of : $\arctan\left(\frac{\ln(1+x)}{1+x}\right)$ How do I find out the series expansion of any inverse ? Note: The inverse of a function $f$...