# Questions tagged [series-expansion]

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

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### Trouble finding inverse of a function

I have the following Mathematica code: ...
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1 vote
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### Expanding a Matrix Vector product in powers of epsilon

I am attempting a perturbation expansion in Mathematica. As part of this, I would like to expand a matrix-vector product where the vectors are given in powers of epsilon. Eventually, I'd like to ...
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### Numerically solving nonlinear PDE $u_t = G(u,u_y,u_{xy},u_{xx}u_{yy})$ with unbounded initial condition

I am trying to numerically solve some nonlinear partial differential equations similar to the example given below, for which I have been unable to obtain stable numerical solutions due to some ...
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### Neglecting higher order terms in a Lagrangian

I have a lagrangian which is modified by variable change. I want to neglect all the 4th order and higher terms in the new lagrangian. The code being used is given below: ...
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### NonlinearFit with series coefficients

I have a set of data: ...
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### How to plot a graph for the solution to a differential equation

I am very new to Mathematica and am struggling to get a plot for a differential equation I need solving. I am doing a simplified version of the lane-emden equation for n=1 so have the follwoing ...
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### Why the coefficient function is very fast

When looking for the coefficients of an desired series, I found that the Coefficient function is very fast compared to other functions and methods. In the following summary, we find the different ...
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### Best way to handle numerical integration and power series with large numbers

Due to the fact that almost everything I do in my research is analytic, I am quite unfamiliar with numeric calculus, so I was wondering if anyone could give me some advice on the most efficient way to ...
64 views

### Why would SeriesCoefficient not work on an inequality

Here is a humble function with a series of powers of $x$, but when I express the function as an inequality it is no longer able to solve. Is there a reason for this behavior? ...
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1 vote
113 views

### How to write code for SeriesCoefficient to work for non integral coefficients?

I have a function of $r$ which I expand at $\infty$ using Series. It is a complicated and messy function, with a parameter $0 \leq \epsilon < 1$. After expansion,...
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### How to use FindSequenceFunction to obtain the general expression of Fourier series?

I want to get cosine series of the following functions. $f(x)=\left\{\begin{array}{cc}\cos x, & 0 \leqslant x<\frac{\pi}{2} \\ 0, & \frac{\pi}{2} \leqslant x \leqslant \pi\end{array}\right.$...
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104 views

### Splitting a sum in parts for finding a telescoping sum?

Have here a sum of which it can be split into several sums. How to do this from the sum notation itself at once ? Note :I do not want to use the command "Apart" to first split the fraction ...
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### Series solution of a differential equation

Calculate the series solution of a differential equation: $\frac{\mathrm{d} y}{\mathrm{~d} x}=-y-x$, ( $\left.y\right|_{x=0}=2$) AsymptoticDsolvevalue can calculate ...
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### How to make a definition and evalulation for a sequence [closed]

Here a example of sequenze (unfortanely i could not copy/paste as Latex ?) How to input this in MMA ? EDIT: example 2 : for n = 8
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### Series for $(1+x)^{m}$ with specific notation

I'm trying to get mathematicas series function for $(1+x)^{m}$ to output a result that look like this: $(1+x)^{m} = \sum_{n=0}^{\infty} \frac{m !}{n !(m-n) !}x^{n}$ However, ...
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### Series for Sin[x] with specific notation

I'm trying to get mathematicas series function for Sin[x] to output a result that look like this: $\sin x=\sum_{n=0}^{\infty} \frac{(-1)^{n}}{(2 n+1) !} x^{2 n+1}$ ...
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### Result of expansion changes based on when I define a quantity

I have code where I evaluate a series expansion symbolically. I want to do the same thing without explicitly specifying the point before the expansion. Naively, I think this should not change my ...
125 views

### Solving coupled ODE by analyzing solution near zero

This question is related to an earlier question I had asked, regarding coupled first order odes. I'll add the system of odes with their boundary conditions again here. . The comments for the previous ...
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### How does Mathematica take a Series expansion at Infinity?

I have a program that requires a series expansion at infinity and at a finite horizon, and I have posted two questions about simplifying these expressions or obtaining the series expansion recently. ...
136 views

### Mathematical Expression takes too long to even display

I have the following expression, that I obtain in the following way: ...
1 vote
80 views

### Series expansion not returning anything

I have a differential equation, which I want to expand as a series at a finite $r$ value - the horizon, and at $\infty$. The functions involved are definitely cumbersome, and I have recreated my code ...
98 views

### Series solution of differential equation

My equation reads: I expand the solution: For example: to zeroth order differential equation reads: where the index i+i is understood modulo 2. At order $\Lambda^4$ equation reads: Proposing the ...
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I am trying to correct some bills for laurent series with mathematica, but the output I am getting at the moment is not the best. For example, I have this function $$\frac{1}{z^2 + 9}$$ to develop at ...