# Questions tagged [series-expansion]

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

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### Why can’t mathematica find this residue?

I am trying to find the residue of the function $$f(z)=(z+1)^2e^{3/z^2}$$ at $z=0$. I tried the following in Mathematica Residue[(z+1)^2*Exp[3/z^2],{z,0}] which ...
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### How can I select the true expansion?

I have a series expansion which gives two results. Series[-(1/ Sqrt[-1 + x + x z1^2 \[Chi]^2]) , {x, 0, 1}] /. y -> x I want only the series which is true. ...
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### Series expansion really slow

UPDATE Seems the problem is associated with the division. I've tried taking the Normal[Series[]] of each numerator and denominator separately, and then again ...
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### Grouping terms in Taylor expansion

I have this code: ...
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### Change in behaviour of Series from 11.1

In 11.0, Series[(1 - Sqrt[1-4z])/2, {z, 1/4, 1}] gives 1/2 - I Sqrt[z-1/4] + O[z-1/4]^(3/2) as one would expect. From 11.1 ...
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### Series with Dedekind eta function does not expand in 11.3

The following expansion works correctly under versions 7, 10.2, 11.0 ...
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### Finding the position of exponents with non-zero coefficients

Suppose that an expansion can be obtained from ...
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### About two point Taylor series expansion

From a comment to a two years old question of mine on MSE, I heard (for first time, I must confess) about two point Taylor series expansions; the commenter gave a link to a "quite" recent paper. ...
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### When to trust Series

I want to evaluate this function near x=1: ...
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### Trying to get a Laurent expansion of a symbolic function

Im trying to find the Laurent expansion of the function $$f(z):=\frac{a-b}{(z-a)(z-b)},\quad\text{for }0<|a|<|b|$$ around $z=0$ in the annulus defined by $A:=\{z\in\Bbb C:|a|<|z|<|b|\}$. ...
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### Series expansion gives different result

I would like to know the leading order of $x$ in the expression $\sqrt{c+x^2-\sqrt{c^2+x^2}}$, where $x>0$ and $c\in \mathbb{R}$. I tried ...
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### Series expansions with negative powers

Here is a minimal example of my problem. I expand a function, f[x], in a Taylor series around a point a == 1/b. The variable <...
279 views

### Guess special function from few power series coefficients

I remember having come across a nifty function that guesses some special functions taking some specific values for its parameters, such that when expanded in a power series, its coefficients match a ...
49 views

### Series expansion using complex variables

Suppose I have a function F[r_]:= A/r + B/r^2 + Conjugate[C]/r^3 with A, B, C being complex numbers and r being a real variable. I would like to series expand ...
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### Solving a mathematical series inequality with mathematica

I have to show that a_n >= b_n for N{0}, Knowing that a > 0 and b > 0. See the picture How can I show the inequality with mathematica? Here is what I tried, but it didn't work (I began Mathematica ...
I am new to Mathematica. I want to produce the Lagrange inversion coefficients by using Bell polynomials. In the following image you can see expressions for the first seven coefficients $A_1$ to $A_7$...