The series-expansion tag has no wiki summary.
2
votes
1answer
61 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 ...
1
vote
0answers
43 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:
...
8
votes
3answers
145 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
66 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 ...
2
votes
1answer
123 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 $1<|z|<2$?
8
votes
0answers
109 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. ...
6
votes
0answers
91 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 ...
5
votes
5answers
301 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
69 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 ...
5
votes
0answers
81 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
55 views
Asymptotic expansion of a list
I am trying to calculate a asymptotic series expansion of a list.
...
0
votes
0answers
66 views
How to have Mathematica find asymptotics with correct asumptions
I'm tried to find a certain expansion of the Hypergeometric1F1 function using Mathematica:
...
9
votes
2answers
203 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 ...
0
votes
1answer
53 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
78 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
126 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) ...
4
votes
2answers
327 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:
...
1
vote
1answer
60 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
166 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
137 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
307 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 ...
6
votes
1answer
346 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, ...
5
votes
3answers
486 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
289 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?
0
votes
2answers
393 views
About generating power series
For an arbitrary function $f(x,y)$ I am defining functions LogMT1 and LogMT2 as follows,
...
2
votes
1answer
161 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
115 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
241 views
Series expansion with irrational power
I need the series expansion of a fairly nasty function and its derivative:
...
3
votes
3answers
238 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
316 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
141 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
369 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 ...
