The series-expansion tag has no wiki summary.
0
votes
1answer
48 views
Retain required terms in asymptotic expansions
I am using Mathematica 8 to do lengthy asymptotic expansions for use in statistics.
In particular I have
$\lambda=\beta+\epsilon+\delta+\gamma+O(n^{-5/2})$
where the first term is of order ...
0
votes
0answers
46 views
Find leading-order asymptotic approximatons to the solution of epsilon y''+Cosh[x]y'- y == 0
I am trying to solve this boundary value problem and obtain the leading-order approximations using asymptotic matching. But I got my solution wrong and I am stuck along the way, struggling to find any ...
4
votes
2answers
73 views
Solution of equation with power series (perturbation)
So I need to use Mathematica to find the solution of $y=x- \epsilon \sin(2y)$ as a power series in terms of $\epsilon$. I'd assume I'd need to create an equation $f=x-y- \epsilon \sin(2y)$, then ...
4
votes
1answer
148 views
Solving an ODE in power series
How do I find a series solution to an ODE?
I do not mean taking the Taylor series of an exact solution; I want to solve nasty nonlinear differential equations locally via plug and chug. Surely, that ...
2
votes
1answer
177 views
Laurent series expansion
Can someone share how to find a Laurent series expansion of
$$f(z)=\frac{1}{(z^2-1)(z^2-4)}$$
centered at zero on the annular disk $1<|z|<2$?
0
votes
2answers
413 views
About generating power series
For an arbitrary function $f(x,y)$ I am defining functions LogMT1 and LogMT2 as follows,
...
1
vote
1answer
87 views
Switching the axis of a plot [duplicate]
I have a plot but the x and y axis need to be switched. The problem is that I can't explicitly solve for the other so I can change the axis.
...
2
votes
1answer
73 views
from complex function to a series
How can I express this complex function as a series?
Log[
(1 - E^((I Pi (1 - a))/(b - a)) z)/
(1 - E^(-((I Pi (1 - a))/(b - a))) z)
]
Where ...
6
votes
1answer
379 views
How to expand a function into a power series with negative powers?
Is there any way to expand this expression
a+b(1-Exp[-T/(b c)]/(z-Exp[-T/ (b c)])
(where a, ...
9
votes
2answers
272 views
InverseSeries of multiple variables and multiple equations
CONTEXT
Let us consider a bit of the Universe in which we draw spheres
(see a high resolution image here). Astronomers have shown that the density within these spheres
could be predicted quite ...
12
votes
4answers
508 views
Evaluation of a triple sum does not finish in reasonable time
I'm trying to compute the following triple sum, but no result is produced within a reasonable amount of time. What to do?
...
9
votes
2answers
224 views
Find closed form expression for series expansion coefficients [duplicate]
Is there a built-in function that will find a general expression for the coefficient of the series expansion of a function?
Series will only give the explicit ...
1
vote
0answers
44 views
Decimal representations of analytic values in an expansion
I have a solution to an ODE (which I call sol), which I would like to expand in terms of Log[1+x] around x=-1. I thought that:
...
2
votes
1answer
69 views
The proper way to write the input for a certain series
Mathematica tells the series below doesn't converge. I think it converges. What would the
proper way to write things be as an input?
...
8
votes
3answers
150 views
Declaration of abstract matrices to perform series expansion on them
I would like to have abstract matrices M and S to get out the coefficients of matrix power series however it treats M and S as numbers even if i checked that M.S - S.M != 0. I attach my code below:
...
-1
votes
1answer
69 views
How can we suppress the asymptotic notation in Series? [closed]
Series expands a function, and also gives an idea of the asymptotic bounds of the function:
Series[$\frac{1-x^3}{1-x}$] returns: $1 + x + x^2 + O(x)^5$
I'd like ...
0
votes
0answers
77 views
How to have Mathematica find asymptotics with correct asumptions
I'm tried to find a certain expansion of the Hypergeometric1F1 function using Mathematica:
...
6
votes
0answers
93 views
Design considerations behind `O` (a.k.a. BigOh, a.k.a. Landau Order)
This works without any warnings: O[Log[x]].
This raises a warning: O[x^2].
I have a few questions around this:
Why is it a ...
8
votes
0answers
115 views
Why does Mathematica fail to series expand this simple expression?
I wanted to expand the function $(x+2)^{x+2}$ around $x = -1$, that is, using
Series[(x + 2)^(x + 2), {x, -1, 2}]
and Mathematica returns the same expression. ...
5
votes
5answers
352 views
Series expansion in terms of Hermite polynomials
I am trying to expand a polynomial in terms of orthogonal polynomials (in my case, Hermite). Maple has a nice built-in function for this, ChangeBasis.
Is there a ...
1
vote
0answers
75 views
Getting poles of a Gamma functions
Why do the following 2 sequences give different answers?
n = 1.5
Series[Gamma[0.5 - n - x], {x, 0, 2}]
Series[Gamma[-1 - x], {x, 0, 2}]
(..clearly the output from the second expression is ...
4
votes
2answers
337 views
How do I solve N simultaneous equations for N variables?
I have a function:
f[x_] := x + 31 x^3 + 5 x^25
Which I want to find an expansion for:
...
5
votes
0answers
82 views
Expansion of $E(i c \mid m)$ at $c\to\infty$?
Currently, I am using a Windows machine with Mathematica 8. I noticed a difference in a series expansion of the function EllipticE[] in comparison with a result ...
1
vote
1answer
56 views
Asymptotic expansion of a list
I am trying to calculate a asymptotic series expansion of a list.
...
9
votes
2answers
115 views
Unexpected behaviour of SeriesCoefficient?
Following this question/answer I discovered and played with SeriesCoefficient. In particular, I tried
...
0
votes
1answer
56 views
Formatting Equation Output Neatly
I looked around and couldn't find the answer to this anywhere, so I'm sorry if this is a bad question - I'm pretty new to mathematica. I wrote a program to help me compute some annoying series ...
4
votes
0answers
79 views
Proper treatment of roots and powers in Series?
I have the following problem in Mathematica 9 on Linux. I let Mathematica compute the Series expansion:
...
1
vote
0answers
145 views
How can I expand $1/(1-x)$ in series, centered at $x_0=2$ and region $|x-2|>1$? [closed]
Function: $1/(1-x)$
I've already discovered the following:
(1) Series[1/(1-x), {x,0,10}]: expand it centered at $x_0=0$, region $|x|<1$.
(2) ...
1
vote
1answer
62 views
Series command no longer expands arbitrary functions after aborting previous evaluation
I asked Mathematica 9 to execute the SeriesCoefficient command on a rather horrendously complicated expression. After some time I decided to abort the evaluation ...
0
votes
1answer
183 views
Asymptotic expansion, negative powers
The question was inspired by this discussion:
How to expand a function into a power series with negative powers?
I am interested in asymptotic behavior of a function at infinity:
...
6
votes
0answers
140 views
Why does $\frac{\partial}{\partial x}O\left(\left(\frac{1}{x}\right)^0\right)$ equal $O\left(\left(\frac{1}{x}\right)^0\right)$ in a series expansion?
When taking the derivative of a series expansion around a finite point, the $O(x^n)$ part is differentiated as expected. $O(x^n)$ becomes $O(x^{n-1})$ except $O(x^0)$ which stays $O(x^0)$.
When ...
3
votes
2answers
349 views
How to study asymptotic behavior, built-in functions
My question is as follows. Suppose we have a function $f(r)$ and we want to study its asymptotic behavior at infinity ($r\rightarrow \infty$). For example, the function may reduce to $-\frac{a}{r}$ or ...
5
votes
3answers
557 views
Multivariable Taylor expansion does not work as expected
The basic multivariable Taylor expansion formula around a point is as follows:
$$
f(\mathbf r + \mathbf a) = f(\mathbf r) + (\mathbf a \cdot \nabla )f(\mathbf r) + \frac{1}{2!}(\mathbf a \cdot ...
1
vote
1answer
309 views
How can I get a Taylor expansion of the Sin[x] function?
How can I get a Taylor expansion of the Sin[x] function by the power series?
2
votes
1answer
168 views
About high dimensional integrals
I want to be able to do high dimensional integrals like,
(..naively I wrote it as this..)
...
0
votes
0answers
116 views
series expansion
I have a fourth order equation
equation (22)
and I must solve it with respect to delta0 (i.e.: Solve[equation,delta0]) to have a solution for small value of mu1 ...
7
votes
2answers
248 views
Series expansion with irrational power
I need the series expansion of a fairly nasty function and its derivative:
...
3
votes
3answers
243 views
Limiting form of a polynomial expression
When simplifying an expression by hand, a trick that is often used is to remove terms that are lower powers of the independent variable, for instance, as $x \rightarrow \infty$,
$x^2 + x$
becomes ...
0
votes
1answer
334 views
Fourier series of interpolating function result of NDSolve
I am having a tough time formulating the right question but here goes.
I know that solving the pde as in here gives me an interpolating function. I understand that the interpolating function object ...
6
votes
1answer
145 views
Sophistication of Series[…]
I'll give a concrete example and I hope that my general question will be clear.
Say I have three variables, $f$, $g$, $h$, and I know that $f=\mathcal O(x)$, $g=\mathcal O(x^2)$, $h=\mathcal O(x^3)$ ...
8
votes
2answers
388 views
Series expansion of an inverse
I have to find the series expansion of the inverse function of : $\arctan\left(\frac{\ln(1+x)}{1+x}\right)$
How do I find out the series expansion of any inverse ?
Note: The inverse of a function ...
