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

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2
votes
2answers
617 views

About generating power series

For an arbitrary function $f(x,y)$ I am defining functions LogMT1 and LogMT2 as follows, ...
1
vote
1answer
55 views

Reducing a multi-variate polynomial to have terms upto certain degree

I have a polynomial in x and y. I want to keep all the terms with (combined) degree 4. Any pointers will be appreciated. Simple tricks for doing the same with univariate polynomial don't seem to work. ...
8
votes
0answers
146 views

How does Mathematica find a series expansion of expressions containing logarithms when there is a singularity at the expansion point?

I am looking for a good approximation to a function containing logarithms, especially at values close to zero. When I used Mathematica's Series command I found ...
7
votes
0answers
185 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 ...
6
votes
0answers
105 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
0answers
97 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 ...
4
votes
0answers
104 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: ...
2
votes
0answers
109 views

Series expansion: Taylor series takes huge amount of time

I'm working on a notebook, trying to expand the root of a cubic polynomial in Taylor series. When I type: ...
2
votes
0answers
86 views

Expanding a Function in Series works, SeriesCoefficient Doesn't Work

Take the following definitions: ...
2
votes
0answers
103 views

Changing bounds of summation after differentiating symbolic sums

Suppose, I have a function written as Taylor-Maclaurin series f = Sum[c[n]*x^n, {n, 0, Infinity}] Now, I wish to differentiate this expression with respect to ...
1
vote
0answers
54 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: ...
0
votes
0answers
283 views

Solving differential equations with sums (power series)

I have sets of 10 differential equations, but for this purpose I'll demonstrate what I need on one example that can be solved by hand. My equation is this: ...
0
votes
0answers
46 views

Degeneracy problem at the start of a series expansion

I am facing the following problem : I have an equation which could write $$ F(x_1(Y))-F(x_2(Y)) = 0 $$ $x_1$ and $x_2$ are the largest and smallest roots of a cubic equation; their definition ...
0
votes
0answers
184 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 ...
0
votes
0answers
237 views

How to have Mathematica find asymptotics with correct asumptions

I'm tried to find a certain expansion of the Hypergeometric1F1 function using Mathematica: ...