# Tagged Questions

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

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### Puiseux series for algebraic curves

Has anyone implemented a function in Mathematica that computes Puiseux expansions of algebraic curves? Using something like ...
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### Two unrelated questions: 1. Output of Series[] for function, 2. Output conditional answers as if not conditional [closed]

As mentioned in the title, I have two questions. 1. I have code that looks similar to: ...
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### How can I obtain an asymptotic integral expansion at infinity?

I want to find the asymptotic expansion at $x \to \infty$ of the following function: $$I(x) \equiv \int_0^{\pi/2} e^{-xt^3 \cos(t)} dt.$$ To do this I defined ...
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### Subtracting Series

When I input the following $$\sum_{n=0}^{m+1}x[n]-\sum_{n=0}^{m}x[n]$$ which in InputForm is: ...
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### How to turn arbitrary function to polinomial series in Mathematica?

Can I turn any multivariate function into polinomial series in Mathematica? Suppose I have a function Fwd[x_, α_] := x (1/Sin[Pi x/2])^α and wish to express it ...
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### How to reverse irreversible function in Mathematica?

How to reverse formula $y(x)=x (\frac{1}{sin \frac{\pi x}{2}})^\alpha$ i.e. express it as $x = x(y)$ in Mathematica? I did this way ...
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### FourierSinCoefficients extremely slow

I'm just playing with Fourier decomposition of periodic functions. We had a similar example with standing waves and cosines in class, so I tried to expand a triangle wave in sines. This is what I came ...
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### Contour Integration along a contour containing two branch points

I need to compute following contour integrations: $$f(u)=\oint_\alpha dz \sqrt{z^3+z+u} \qquad ; \qquad g(u)=\oint_\beta dz \sqrt{z^3+z+u}$$ In which $\alpha$ and $\beta$ are two contours in ...
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### Series with a specified number of terms

I'm doing calculations with Series where I don't know the power of the leading order term. I would like to keep a specified number of terms, but since I don't know the leading order this is proving ...
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### Expansion of a hypergeometric function takes ages with Mathematica 9 and 10 (regression?)

Mathematica 8 (Linux version) can evaluate AbsoluteTiming[Series[Hypergeometric2F1[1, 1 - eps/2, 3 - eps, 1/2], {eps, 0, 0}]] in no time. On one of the ...
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### Series expansion of NDSolve solution produced by shooting method

The ODE I need to solve is ...
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### How to obtain Laurent series coefficients of an (almost) arbitrary function?

I have observed that Series in Mathematica assumes that the given function is smooth in the point around which one wants to perform series expansion. For instance: ...
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### Extract a part of Series

If I have the output of Series, in terms of powers of my variable $x$, what is the quickest way to extract a part of the series, say for example the terms from $x^2$ to $x^5$, excluding those with ...
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### Extract a term of Series output

Say I have the output of series, with all the coefficients of the different powers of my variable $x$. What is the quickest way of extracting the coefficient of the $n$-th power of $x$?
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### Truncate a sum in a 'smart' way

Consider a series like this: $$\sum_{n=1}^{\infty} (c_n r^{2-n/2}+d_n r^{-n/2})$$ Sum[c[n]r^(2-n/2)+d[n]r^(-n/2),{n,Infinity}] I want, now, to keep only the ...
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### Series identity with binomial coefficients [duplicate]

I have this apparently simple equation: ...
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### Series expression of a Root object

I was wondering if it is possible to get Mathematica to return a series approximation of a Root object. Example: I want a series representation of x in terms of <...
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### Linearization of differential equations

I was wondering if one could define an operator such that, when I give a certain number of (differential) equations as an output, and an "equilibrium" value for each of the variables, it returns the ...
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### Can't get solution to a system of recurrence equeations

I would be grateful if someone could help me with this problem. I define two series recursively, thus: ...
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### Isolating cross terms

I have a set of expressions that contains terms like $\frac{1}{(x + a + b)(c+d)}$. I would like to simplify the denominator so that products of $a,b,c,d$ are dropped, but $x c$ and $x d$ are kept. ...
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### Changing default behavior of Series to give slightly different SeriesData

I am working with complicated expressions expr that contains the symbolic function f[x] which I know to have a pole at ...