Questions tagged [series-expansion]

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

Filter by
Sorted by
Tagged with
1 vote
1 answer
105 views

Trouble finding inverse of a function

I have the following Mathematica code: ...
  • 585
1 vote
3 answers
145 views

Series expansion of the integral from its numerical values

I have already asked a similar question regarding approximating Taylor series of the function from noisy data. This is another example I am having trouble with. Consider the integral $$I(x)=\int_0^1\...
  • 73
3 votes
1 answer
118 views

How to do the series expansion of terms with PolyLog faster?

I have the following expression that I need to series expand, around t=0 (PolyLog[3, 1 + Tanh[J t]] - PolyLog[3, 1 - Tanh[J t]])Tanh[J t] The amount of time to ...
  • 155
3 votes
1 answer
56 views

Collecting even power terms in Ising problem

I am trying to solve the Ising model for $4 \times 4$ square lattice without a magnetic field. The calculation involved evaluating the expression below, After writing the code as ...
  • 115
0 votes
0 answers
43 views

Unable to expand this solution in the form of Hypergeometric function

I want to write this solution into hyper geometric function ...
0 votes
0 answers
39 views

Taylor series expansion of a challeging type of polynomial with two summation signs

I have a few questions about series expansions of a particular and difficult type of polynomial written in terms of two summations signs. It should be remarked that I have also read Mathematica's ...
3 votes
1 answer
105 views

Calculating power series of quantum operators on kets

I am using the "Quantum" add-on package to perform some quantum mechanical calculations using SU(1,1) generators. The code that I've developed reads ...
  • 727
1 vote
1 answer
108 views

Problem in getting coefficients list of power series solution of y''[x]*y'[InverseFunction[y][x]] - y'[x] == 0?

I have tried to get solution of the following ODE: y''[x]*y'[InverseFunction[y][x]] - y'[x] == 0 Using the code given below, the solution is a formal power series ...
6 votes
1 answer
161 views

How to get more terms with the Series[] expansion of InverseErf[x] around x=1?

The inverse error function, which is given by InverseErf[x], is quite important in statistics as it gives the confidence levels around a 1D Gaussian, for example ...
  • 1,192
3 votes
0 answers
124 views

Cannot Understand nth Derivative of x/ArcTan[x]

The nth derivative of x/ArcTan[x]: f[x_, n_] = D[x/ArcTan[x], {x, n}] Evaluates to: I cannot get this general from to return ...
0 votes
0 answers
67 views

How to do this recursion relation in Mathematica effectively?

I have a function $h_{\Delta,l}(r,\eta)$ satisfying \begin{equation} h_{\Delta,l}(r,\eta)=\tilde{h}_{l}(r,\eta)+\sum_{k}\frac{c(k)}{\Delta-(1-l-k)}r^{k}h_{1-l+k,l+k}(r,\eta) \end{equation} where $k$ ...
  • 51
1 vote
1 answer
71 views

Series Expansion of EllipticNomeQ differs from older Mathematica Version

I am trying to follow the numerical approach on how to calculate EllipticE and EllipticK following this paper. In there on ...
  • 4,467
0 votes
0 answers
37 views

Scaling a variable multiplied by power series is not giving expected output

I have a power series getting multiplied by a variable, which gets scaled by the small parameter used in the power series. As an example, in the following dummy series: ...
6 votes
3 answers
127 views

Extracting a logarithmic divergence of an expression using Series

Consider the following expression: ...
  • 1,249
2 votes
1 answer
106 views

Formal variables no longer simplifying well on new Mathematica version?

I work with a lot of formula manipulation, modular forms etc. For example, the Dedekind eta function comes up a lot, and I'm often interested in the following sort of code: ...
  • 1,307
0 votes
0 answers
73 views

Mathematica 13.0 appears to automatically reverse nested series which contain logarithms. Is there a way to prevent this behavior?

When performing manipulations on nested series, I need the series to retain the nesting order I originally defined. In Mathematica versions 8.0 and 10.4, this was almost always the default behavior. ...
  • 195
0 votes
1 answer
127 views

Can Mathematica solve an ode asymptotically as x goes to infinity?

Given the following ode for $x\rightarrow\infty$: $$\left(x f(x)^3 \left(\frac{(x f^\prime)^\prime}{x}\right)^\prime\right)^\prime=0,$$ in the sense of "asymptotics", the equal sign is ...
0 votes
0 answers
36 views

Plotting contours of a two-variable function containing a sum

I'm trying to use Mathematica to plot contours of a rather intricate two-variable function. The equation describes the velocity profile for laminar flow in a tube of rectangular section, namely: $$ {w^...
  • 21
4 votes
1 answer
63 views

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 ...
  • 79
4 votes
2 answers
150 views

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 ...
  • 141
6 votes
3 answers
327 views

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: ...
  • 585
0 votes
1 answer
64 views

NonlinearFit with series coefficients

I have a set of data: ...
0 votes
1 answer
76 views

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 ...
4 votes
0 answers
61 views

Calculate an n-order determinant by FindSequenceFunction

Calculate an n-order determinant: $\left|\begin{array}{cccccc}1 & 2 & 3 & \cdots & n-1 & n \\ n & 1 & 2 & \cdots & n-2 & n-1 \\ n-1 & n & 1 & \cdots ...
  • 1,513
2 votes
2 answers
100 views

Using the generalised binomial theorem to expand an expression

I would like to use Mathematica to compute the following expansion: $(1+x)^\rho= 1 + \rho x +\dots$ for some $|\rho|<1$ as for example explained here. I tried the Series expansion functions ...
  • 473
1 vote
1 answer
80 views

Taylor expand around a vector

I have a matrix $A(\vec{v})$ whose entries are scalar functions of a vector $\vec{v}=(v_{x},v_{y})$. To be concrete I have something like $A=\begin{pmatrix}f_{1}(\vec{v})& f_{2}(\vec{v})\\f_{3}(\...
  • 153
5 votes
1 answer
93 views

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 ...
5 votes
2 answers
182 views

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 ...
2 votes
1 answer
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? ...
  • 717
1 vote
2 answers
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,...
5 votes
2 answers
162 views

Assumptions for FourierSeries

I want to calculate the Fourier series of the following function. $u(t)=\left\{\begin{array}{lc}0, & -\frac{T}{2} \leqslant t<-\frac{\tau}{2} \\ h, & -\frac{\tau}{2} \leqslant t<\frac{\...
  • 1,513
0 votes
1 answer
63 views

Successive solutions using previously found [closed]

is there a way to use previous calculated values of solve? solving equations based on asymptotic expansion $x^2+x-\varepsilon=0$ $x=x_0+\varepsilon x_1 + \varepsilon^2 x_2 + \varepsilon^3 x_3$ ...
  • 103
2 votes
3 answers
129 views

FindSequenceFunction on trigonometric series

I want to get the sine series general expression of the following two functions by FindSequenceFunction. (1) $f(x)=\left\{\begin{array}{l}0,-2 \leqslant x<0, \\ ...
  • 1,513
-1 votes
2 answers
81 views

How to use FindSequenceFunction to obtain the general expression of Fourier series?

I want to get cosine series of the following functions. $f(x)=\left\{\begin{array}{cc}\cos x, & 0 \leqslant x<\frac{\pi}{2} \\ 0, & \frac{\pi}{2} \leqslant x \leqslant \pi\end{array}\right.$...
  • 1,513
0 votes
1 answer
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 ...
  • 649
3 votes
2 answers
176 views

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 ...
  • 1,513
0 votes
3 answers
131 views

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
  • 649
2 votes
2 answers
115 views

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, ...
  • 1,513
2 votes
2 answers
243 views

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: $\sin x=\sum_{n=0}^{\infty} \frac{(-1)^{n}}{(2 n+1) !} x^{2 n+1}$ ...
  • 1,513
6 votes
1 answer
186 views

Getting terms and only evaluate specific parts of a series

How to write the first five terms of this series in the following form by MMA code? $\sum_{n=1}^{\infty} \frac{1 \cdot 3 \cdot \cdots \cdot(2 n-1)}{2 \cdot 4 \cdot \cdots \cdot 2 n}= \frac{1}{2}+\frac{...
  • 1,513
2 votes
3 answers
199 views

How to map integration and multiplication to a serie?

*For further study of series, they can be put into a different form. Normal[Series[1/(1 - x), {x, 0, 10}]] This serie 1/(1-x) = 1 + x + ... ,must be first ...
  • 649
0 votes
0 answers
141 views

How to get the n-order Taylor expansion of bivariate function?

I want to get the n-order Taylor expansion of a bivariate function at point (x0,y0): f[x_, y_]: = E^(x + y); {x0,y0}={0,0}; The result calculated by hand is: $...
  • 1,513
0 votes
0 answers
40 views

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 ...
2 votes
1 answer
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 ...
  • 73
0 votes
1 answer
118 views

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. ...
0 votes
0 answers
136 views

Mathematical Expression takes too long to even display

I have the following expression, that I obtain in the following way: ...
1 vote
1 answer
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 ...
0 votes
0 answers
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 ...
  • 235
6 votes
1 answer
207 views

Using Integrate and then Series seem to produce a wrong result

Run this: ...
0 votes
1 answer
72 views

Series development of laurent in a defined domain

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 ...
  • 121

1
2 3 4 5
17