# Tagged Questions

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

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### Taylor series representation function? [duplicate]

Is there a built in Taylor series representation function in Wolfram Mathematica? For Example: ...
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### Interpretation of a function

I know this is not great, as far as a question, but I came across this function, ...
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### Finding an analytic solution of a cubic equation

I have been trying to solve a cubic equation $$y=zy^3 + z$$ in $y$ – that is, my desired result is a function $y(z)$ satisfying the equation. Now, there are three solutions of this equation and ...
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### Series of a hypergeometric function

Let $n>2$ be odd, and let $x\in [0,1]$. I would like to calculate the Taylor expansion of $$x^{2-n} \, _2F_1\left(-\frac{n}{2}-1,-n;2-\frac{n}{2};x^2\right)$$ at $x=1$ leaving $n$ non specified....
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### Weird SeriesData behavior?

I was trying to calculate the determinant of a matrix whose elements are truncated series. As a result I obtained an expression like this: ...
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### Differentiation and series expansion of dot product - inconsistent results

If I differentiate a dot product, I get the result I expect D[a.b[x], x] (* a.b'[x] *) However, a series expansion of the same expression gives a very different ...
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### Series expansion of $(x;x)_\infty$ at $x=1^-$?

The so called Euler function is implemented in Mathematica as QPochhammer[x, x] I have been trying to obtain its leading behavior for $x\to 1$ from below. ...
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### How can I make Mathematica list the terms in this series?

I am using perturbation theory to solve a problem of the following form: $$R(h,\theta)f(\theta) = h g(\theta) = 0$$ where $h$ is small, and I assume $$\theta = \sum_{i=0}^\infty \theta_i h^i$$ ...
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### Automation of Perturbation Solution

I'm trying to solve an equation of the form $$R(\theta)f(\theta)+hg(\theta) = 0$$ for small $h$, where $R$, $f$, and $g$ are functions. I've assumed a power series expansion for $\theta$ in terms ...
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### Behavior of solution to a ODE near a singular point [closed]

I want to see how the solution to the following ODE looks near z=z0. ...
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### Series expansion in Infinity issue with Zeta(s) function

With this code: Series[Zeta[s], {s, Infinity, #}] & /@ Range[10] // MatrixForm Series expansion for the Zeta(s) ...
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### OEIS A144311 Generating function

I'm looking for a way to use calculate OEIS A144311 efficiently in Mathematica. First, let's define the series. In one sense or another, this series considers the number between "relative" twin ...
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### Maclaurin Series Help [closed]

My problem is to numerically approximate the series (1 - Cos[x])/x over the interval [0,1]. I typed it into Mathematica as so: ...
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### Can highlight an expression in mathematica in an expansion?

I ask mathematica to make an expansion of some expression. Is there a way to ask mathematica to highlight all terms that, say, goes by x^3 since it is really hard to find them? E.g. ...
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### Ramanujan's asymptotic formula for $p(n)$ [closed]

The following expression is the exact formula of partition function. Ramanujan's asymptotic formula for $p(n)$ is following $$p(n)\sim\frac{1}{4n \sqrt{3}}e^{\pi \sqrt{2n/3}}$$ Can I use ...
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### Bug in Series[Pochhammer[1+n, n], {n,Infinity,1}]?

The function Pochhammer[1 + n, n] tends to infinity. We have ...
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### Find the function $f(x)$ by using its fourier expansion

It is easy to find the fourier coefficient and fourier expansion of $f(x)$ function. But I want solve the inverse problem by using Mathematica How to find the function $f(x)$, if I know its ...
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### Unexpected imaginary term in the asymptotic expansion of DawsonF

FullSimplify[Series[2 DawsonF[x], {x, âˆž, 8}]] (* -I Exp[-x^2] âˆšÏ€ + (1/x + 1/(2 x^3) + 3/(4 x^5) + 15/(8 x^7) + O[1/x]^9) *) What is the reason the term ...
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### A series in powers of $(a-z)$ instead of $(z-a)$

Sometimes it is more convenient to find a series expansion (e.g., Taylor, Laurent, Puiseux, ...) in powers of $(a-z)$ than in powers of $(z-a)$. For instance, the command ...
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### break down the function

I am using Series function, but I found that it cost too much time. Since the Series function is Taylor expansion and I only need first order, I want to break down the code, so I can make it faster <...
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### Sum of Infinite convergent series

I have a series as Sum[(x^1 - (x - 1)^1) (b^Log[(1 + (x))]), {x, 1, Infinity}] which is convergent when b=0.3 and ...
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### Is there a compact way to Taylor expand all the terms in the equation?

For example a vector: ...
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### Problem with solving a system of differential equations [closed]

I am trying to reproduce a result that is part of a derivation of the flow due to a rotating disk. I have as given this system of differential equations. (In these equations primes indicate ...
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### How do I get Series[] as a functional, rather than as an expression (i.e. to avoid the dummy variable)?

How can I write an equivalent to Series that doesn't require a dummy variable? Note that the series should be constructed before the evaluation point is supplied, ...
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### Polynomial kernel expansion

I am trying to calculate the polynomial kernel expansion using Mathematica. I have tried the Expand and Simplify functions with ...
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### How to expand an infinite product?

How can I use Mathematica to expand such a product (only need a finite number of terms): $$\prod^{\infty}_{n=1}\frac{({1-yq^{n+1}})({1-y^{-1}q^n})}{(1-q^n)^2}$$
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### Successive Series Expansion Bug (?)

I've found what appears to be a bug in MMA related to taking successive series expansions. I'm providing this minimal example and post as other posts didn't appear to address the issue I found. In ...
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### Multivariables series expansion up to some power of all the variables [duplicate]

I have a function f[x, y, z] that I would like to expand up to a given power of xyz. For now, I am using ...
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### How can I calculate the root of any order of power series

How can I calculate the root of any order of power series with Mathematica. Here I insert every quantity by hand. But I want to give a, ...
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### Engel expansion

How do I do an Engel expansion in Mathematica? And find the unique non-decreasing sequence of positive integers $\{ a_1 ,a_2,a_3,\dots \}$ , such \frac{e}{\pi}=\frac{1}{a_1}+\frac{1}{a_1 a_2}+\...
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### Easier way to calculate Taylor remainder in 2nd order series

At the moment I have implemented the code for a Taylor 2nd order series for the function in three variables: $x_3^3+\frac{x_1-x_2}{x_1+x_2}$ The code builds on following expression: ...
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### Power series expansion

I am asking Mathematica for the first 5 terms in a power series expansion like this: ...